Variants on Alexandrov reflection principle and other applications of maximum principle

Ricardo Sa Earp; Eric Toubiana

Séminaire de théorie spectrale et géométrie (2000-2001)

  • Volume: 19, page 93-121
  • ISSN: 1624-5458

How to cite

top

Sa Earp, Ricardo, and Toubiana, Eric. "Variants on Alexandrov reflection principle and other applications of maximum principle." Séminaire de théorie spectrale et géométrie 19 (2000-2001): 93-121. <http://eudml.org/doc/114461>.

@article{SaEarp2000-2001,
author = {Sa Earp, Ricardo, Toubiana, Eric},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {Alexandrov reflection principle; maximum principle},
language = {eng},
pages = {93-121},
publisher = {Institut Fourier},
title = {Variants on Alexandrov reflection principle and other applications of maximum principle},
url = {http://eudml.org/doc/114461},
volume = {19},
year = {2000-2001},
}

TY - JOUR
AU - Sa Earp, Ricardo
AU - Toubiana, Eric
TI - Variants on Alexandrov reflection principle and other applications of maximum principle
JO - Séminaire de théorie spectrale et géométrie
PY - 2000-2001
PB - Institut Fourier
VL - 19
SP - 93
EP - 121
LA - eng
KW - Alexandrov reflection principle; maximum principle
UR - http://eudml.org/doc/114461
ER -

References

top
  1. [1] U. Abresch. Constant mean curvature tori in terms of elliptic fonctions. J. Reine Ang. Math. 374,169-192 ( 1987) Zbl0597.53003MR876223
  2. [2] R. Aiyama and K. Akutagawa. Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space, J. Math. Soc. Japan, 52, no.4, 877-898 ( 2000). Zbl0995.53047MR1774634
  3. [3] R. Aiyama and K. Akutagawa. Kenmotsu type representation formula for surfaces with prescribed mean curvature in the 3 sphere, Tohoku Math. J. 52, 95-105 ( 2000). Zbl1008.53012MR1740545
  4. [4] A.D. Alexandrov. Uniqueness theorems for surfaces in the large. I, (Russian) Vestnik Leningrad Univ. Math. 11,5-17 ( 1956). Zbl0122.39601MR86338
  5. [5] T. AubinSome nonlinear problems in Riemannian geometry. Springer ( 1998). Zbl0896.53003MR1636569
  6. [6] J.L. Barbosa. Constant mean curvature surfaces boundedby a plane curve. Mat. Contemp. 1,3-15 ( 1991). Zbl0854.53010MR1304297
  7. [7] J.L. Barbosa and R. Bérard. Eigenvalue and "twisted" eigenvalues problems, applications to CMC- surfaces. To appear in J. Math. Pures and Appl. Zbl0958.58006
  8. [8] J.L. Barbosa, R. Sa Earp. New results on prescribed mean curvature hypersurfacesin Space Forms. An Acad. Bras. Cl. 67, No 1,1-5 ( 1995). Zbl0828.53053
  9. [9] J.L. Barbosa and R. Sa Earp. Prescribed mean curvature hypersurfaces in H n+1 (-1 ) with convexplanar boundary, I. Geom. Dedicata, 71, 61-74 ( 1998). Zbl0922.53023MR1624726
  10. [10] J.L. Barbosa and R. Sa Earp. Prescribed mean curvature hypersurfaces in Hn+1 with convex planar boundary, II. Séminaire de théorie spectrale et géométrie de Grenoble 16, 43-79 ( 1998). Zbl0942.53044
  11. [11] P. Bérard and L. Hauswirth. General curvature estimatesfor stable H-surfaces immersed into space form. J. Math. Pures Appl. 78, 667-700 ( 1999). Zbl0960.53033MR1711051
  12. [12] R. Bérard, L. Lima and W. Rossman. Index growth of hypersurfaces with constant mean curvature. To appear in Math. Z. Zbl0998.53005MR1879330
  13. [13] H. Brezis and J.-M. Coron. Multiple solutions of H-systems and Rellich's conjecture. Commun. Pures Appl. Math. XXXVII, 149-187, 1984. Zbl0537.49022MR733715
  14. [14] A.I. Bobenko. All constant mean curvature tori in R3, S3, H3 in terms of elliptic functions. Math. Ann. 290,209-245 ( 1991). Zbl0711.53007MR1109632
  15. [15] F. Braga Brito and R. Sa Earp. Geometrie configurations of constant mean curvature surfaces with planar boundary. An. Acad. Bras. Ci. 63, No 1, 5-19 ( 1991). Zbl0803.53011MR1115489
  16. [16] F. Braga Brito, W. Meeks III, H. Rosenberg and R. Sa Earp. Structure theorems for constant mean curvature surfaces bounded by a planar curve. Indiana Univ. Math. J. 40, No 1, 333 343 ( 1991). Zbl0759.53003MR1101235
  17. [17] F. Braga Brito and R. Sa Earp. On the Structure of certain Weingarten surfaces with boundary a circle. An. Fac. Sci. Toulouse VI, No 2, 243-255 ( 1997). Zbl0901.53003MR1611824
  18. [18] R. Bryant. Surfaces of mean curvature one in hyperbolic space, Asterisque 154-155 , Soc. Math de France, 321-347 ( 1987). Zbl0635.53047MR955072
  19. [19] R. Bryant. Complex analysis and a class of Weingarten surfaces. Preprint. Zbl17.0045.03
  20. [20] L. Caffarelli, B. Gidas and J. Spruck. Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math. XLII, 271-297 ( 1989). Zbl0702.35085MR982351
  21. [21] L. Caffarelli, L. Nirenberg, J. Spruck. The Dirichlet problemfor nonlinear second-order elliptic equations III. Functions of the eigenvalues of the Hessian. Acta Math. 155, 261-301 ( 1985). Zbl0654.35031MR806416
  22. [22] L. Caffarelli, L. Nirenberg, J. Spruck. Nonlinear second-order elliptic equations V. The Dirichlet problem for Weingarten surfaces. Comm. Pure Appl. Math. XLI, 47-70 ( 1988). Zbl0672.35028MR917124
  23. [23] P. Castillon. Sur les sous-variétés à courbure moyenne constante dans l'espace hyerbolique. Doctoral Thesis, Université Joseph Fourier (Grenoble I) ( 1995). 
  24. [24] S.S. Chern. On special W-surface. Trans. Amer. Math. Soc. 783-786 ( 1955). Zbl0067.13801
  25. [25] R. Collin, Topologie et courbure des surfaces minima les proprement plongées de R3. Ann. Math. 2nd Series 145, 1-31 ( 1997). Zbl0886.53008MR1432035
  26. [26] R. Collin, L. Hauswirth and H. Rosenberg. The geometry of finite topology Bryant surfaces.To appear in Annals of mathematics. Zbl1066.53019
  27. [27] S.Y. Cheng and S.-T. Yau. Differential equations on Riemannian manifolds and their geometric applications. Comm. Pure Appl. Math. XXVIII, 333-354 ( 1975). Zbl0312.53031MR385749
  28. [28] M. Dajczer and M. Do Carmo. Helicoidal surfaces with constant mean curvature. Tôhoku Math J. 34 , 425-435 ( 1982). Zbl0501.53003MR676120
  29. [29] M.P. Do Carmo, H.B. Jr. LawsonOn Alexandrov - Bernstein theorems in hyperbolic space. Duke Math. J. 50, No. 4 ( 1983). Zbl0534.53049MR726314
  30. [30] M. Do Carmo, J. Gomes, G. Thorbergsson. The influence of the boundary behaviour on hypersurfaces with constant mean curvature in Hn+1. Comm. Math. Helvitici 61, 429-491 ( 1986). Zbl0614.53046MR860133
  31. [31] F. Duzaar and K. Steffen. The Plateau problem for parametric surfaces with prescribed mean curvature In: Geometric Analysis and Calculus of Variations (edited by J. Jürgen), pp.13-70, International Press ( 1996). Zbl0935.53007MR1449402
  32. [32] R. Finn. Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature. J.Analyse Math.14, 139-160 ( 1965). Zbl0163.34604MR188909
  33. [33] B. Gidas, W-M Ni and L. Nirenberg. Symmetry and related properties via the maximum principle. Commun. Math. Phys. 68, 209-243 ( 1979). Zbl0425.35020MR544879
  34. [34] D. Gilbarg and N.S. Trudinger. Elliptic partial differential equations of second order. Springer ( l983). Zbl0562.35001
  35. [35] J.M. Gomes. Sobre hipersuperficies comcurvatura média constante no espaço hiperbólico. Doctoral thesis, IMPA ( 1985). 
  36. [36] R.D. Gulliver. The Plateau problem for surfaces of prescribed mean curvature in a Riemannian manifold. J. Diff. Geom. 8, 317-330 ( 1972). Zbl0275.53033MR341260
  37. [37] R.D. Gulliver. Regularity of minimizing surfaces of prescribed mean curvature. Ann. of Math. 97, No. 2, 275-305 ( 1973). Zbl0246.53053MR317188
  38. [38] P. Hartman, W. Wintner. Umbilical points and W-surfaces. Amer. J. Math. 76, 502-508 ( 1954). Zbl0055.39601MR63082
  39. [39] E. Hebey. Introduction à l'analyse non linéaire sur les variétés. Diderot Editeur ( 1997). Zbl0918.58001
  40. [40] S. Hildebrandt. On the Plateau problem for surfaces of constant mean curvature.Commun. Pure Appl. Math. XXIII, 97-114 ( 1970). Zbl0181.38703MR256276
  41. [41] D. Hoffman and H. Karcher. Complete embedded surfaces of finite total curvature. Geometry V (R. Osserman, ed.), Springer, 5-93 ( 1997). Zbl0890.53001MR1490038
  42. [42] J. Hounie and M.L. Leite. The maximum principle for hypersurfaces with vanishing curvature functions. J. Diff. Geom. 41, 247-258 ( 1995). Zbl0821.53007MR1331967
  43. [43] J. Hounie and M.L. Leite. Two-ended hypersurfaces with zero scalar curvature. Indiana Univ. Math. J. 48, No. 3, 867-882 ( 1999). Zbl0929.53033MR1736975
  44. [44] D. Hoffman and W. Meeks. The strong halfspace theorem for minimal surfaces. Invent iones Math. 101, 373-377 ( 1990). Zbl0722.53054MR1062966
  45. [45] H. Hopf. Differential geometry in the large. Lect. Notes in Math., Springer, 1000 ( 1983). Zbl0526.53002MR707850
  46. [46] W-Y Hsiang. On generalization of theorems of A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature. Duke Math. J. 49, No.3 ( 1982). Zbl0496.53006MR672494
  47. [47] N. Kapouleas. Complete constant mean curvature surfaces in Euclidean three space. Ann. Math. 131, 239-330 ( 1990). Zbl0699.53007MR1043269
  48. [48] N. Kapouleas. Compact constant mean curvature surfaces in Euclidean three-space. J. Diff. Geom. 33, 683-715 ( 1991). Zbl0727.53063MR1100207
  49. [49] K. Kenmotsu. Weierstrass formula for surfaces of prescribed mean curvature, Math. Ann. 245, 89-99 ( 1979). Zbl0402.53002MR552581
  50. [50] N. Korevaar, R. Kusner and B. Solomon. The structure of complete embedded surfaces with constant mean curvature. J. Diff. Geom. 30, 465-503 ( 1989). Zbl0726.53007MR1010168
  51. [51] N. Korevaar, R. Kusner, W.H. Meeks III and B. Solomon. Constant mean curvature surfacesin hyperbolic Space. Amer. J. Math. 114, 1-143 ( 1992). Zbl0757.53032MR1147718
  52. [52] M. Koiso, Symmetry of hypersurfaces of constant mean curvature with symmetric boundary. Math. Z. 191,567-574 ( 1986). Zbl0563.53007MR832814
  53. [53] M. Kokubu. Weierstrass representation for minimal surfaces in hyperbolic space, Tohoku Math. J. (2) 49, no. 3, 367-377 ( 1997). Zbl0912.53041MR1464184
  54. [54] N. Korevaar. Sphere theorems via Alexandrov for constant Weingarten curvature hyper surfaces-appendix to a note of A. Ros. J. Diff. Geom. 27, 221-223 ( 1988). Zbl0638.53052
  55. [55] N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen. Refined asymptotics for constant scalar curvature metries with isolated singularities. Invent. Math. 135, 233-272 ( 1999). Zbl0958.53032MR1666838
  56. [56] R. Kusner. Global Geometry of Extremal Surfaces in Three-Space, Doctoral Thesis, University of California, Berkeley ( 1985). 
  57. [57] B. Lawson. Complete minimal surfaces in S3. Ann. Math. 92, 335-374 ( 1970). Zbl0205.52001MR270280
  58. [58] B. Lawson. Lectures on minimal submanifolds. Secon edition, Publish or Perish ( 1980). Zbl0434.53006
  59. [59] R. Langevin and H. Rosenberg. A maximum principle at infinity for minimal surfaces and applications. Duke Math. J. 57, 819-828 ( 1988). Zbl0667.49024MR975123
  60. [60] C. LiMononicity and symmetry of solutions of fully nonlinear elliptic equations on bounded domains. Commun. Part. Diff. Eq. 16, No 2&3, 491-526 ( 1991). Zbl0735.35005MR1104108
  61. [61] C. LiMononicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains. Commun. Part. Diff. Eq. 16, No 4&5, 585-615 ( 1991). Zbl0741.35014MR1113099
  62. [62] G. Levitt, H. Rosenberg. Symmetry of constant mean curvature hypersurfaces in hyperbolic space. Duke Math. J. 52, No. 1 ( 1985). Zbl0584.53027MR791291
  63. [63] R. López and S. Montiel, Constant mean curvalure dises with bounded area. Proc. Amer Math. Soc. 123, 1555-1558 ( 1995). Zbl0840.53006MR1286001
  64. [64] F.J. Lopez and A. Ros. On embedded complete minimal surfaces of genus zero. J. Diff. Geom. 33, No 1, 293 300 ( 1991). Zbl0719.53004MR1085145
  65. [65] J. McCuan. Symmetry via spherical reflection. To appear in J. Diff. Anal. Zbl1010.53007MR1794577
  66. [66] W. Meeks III. The topology and geometry of embedded surfaces of constant mean curvature. J. Diff. Geom. 27,539-552 ( 1988). Zbl0617.53007MR940118
  67. [67] W. Meeks III and H. Rosenberg. The maximum principle al infinity for minimal surfaces in flat 3-manifolds. Comm. Math. Helv. 65, 255-270 ( 1990). Zbl0713.53008MR1057243
  68. [68] W. Meeks III and H. Rosenberg. The geometry and conformal structure of properly embedded minimal surfaces of finite topology in F3. Invent. Math. 114, 625-639 ( 1993). Zbl0803.53007MR1244914
  69. [69] W. Meeks III and S.-T. Yau. The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z.179,151-168 ( 1982). Zbl0479.49026MR645492
  70. [70] R. Molzon. Symmetry and overdetermined boundary value problems. Forum Math. 3,143-156 ( 1991). Zbl0789.35118MR1092579
  71. [71] C. Jr. MorreyThe problem of Plateau on a Riemannian manifold. Ann. of Math. 49, No. 4, 807-851, 1948. Zbl0033.39601MR27137
  72. [72] B. Nelli, H. Rosenberg. Some remarks on embedded hypersurfaces in Hyperbolic Space of constant mean curvature and spherical boundary. Ann. Glob. An. and Geom. 13, 23-30 ( 1995) Zbl0831.53039MR1327108
  73. [73] B. Nelli and R. Sa Earp. Some Properties of Hypersurfaces of Prescribed Mean Curvature in Hn+1. Bull. Sc. Math. 120. No 6, 537-553 ( 1996). Zbl0872.53008MR1420970
  74. [74] B. Nelli and J. Spruck. On the existence and uniqueness of constant mean curvature hypersurfaces in hyperbolic space.Geometric Analysis and Calculus of Variations, International Press, J. Jost (Ed.), 253-266 ( 1996). Zbl0936.35069MR1449411
  75. [75] J. Ordóňes. Superficies helicoidais com curvatura constante no espaço de formas tridimensionais. Doctoral Thesis, PUC-Rio ( 1995). 
  76. [76] U. Pinkall and I. Stirling. On the classification of constant mean curvature tori. Ann. Math. 130, 407-451 ( 1989). Zbl0683.53053MR1014929
  77. [77] M.H. Protter and H. F. Weinberger. Maximum principles in differential equations. Elglewood Cliffs., New Jersey Prentice-Hall ( 1967). Zbl0153.13602MR219861
  78. [78] J. Ratcliffe. Foundations of hyperbolic manifolds. Springer ( 1999). Zbl0809.51001MR1299730
  79. [79] H. Rosenberg. Hypersurfaces of constant curvature in space forms. Bull. Sc. Math. 2e série 117, 211 -239 ( 1993). Zbl0787.53046MR1216008
  80. [80] H. Rosenberg. Some recent developments in the theory of properly embedded minimal surfaces in R3. Séminaire Bourbaki, 44ème année, No 759 ( 1991-92). Zbl0789.53003
  81. [81] L. Rodriguez and H. Rosenberg. Half-space theorems for mean curvature one surfaces in hyperbolic space. Proc. Amer. Math. Soc. 126, No 9, 2755-2762 ( 1998). Zbl0904.53041MR1458259
  82. [82] A. Ros and H. Rosenberg. Constant mean curvature surfaces in a half-space with boundary in the boundary of the half-space. J. Diff. Geom. 44, 807-817 ( 1996) Zbl0883.53009MR1438193
  83. [83] H. Rosenberg and R. Sa Earp. Some remarks on surfaces of prescribed mean curvature. Differential Geometry (Symposium in honor of M. do Carmo). Pitman monographs and surveys in Pure and Applied Mathematics, 123-148 ( 1991). Zbl0773.53002MR1173038
  84. [84] H. Rosenberg and R. Sa Earp. Some Structure Theorems for Complete Constant Mean Curvature Surfaces with Boundary a Convex Curve. Proc. Amer. Math. Soc. 113, No 4, 1045-1053 ( 1991). Zbl0748.53003MR1072337
  85. [85] H. Rosenberg and R. Sa Earp. The geometry of properly embedded special surfaces in R3; e.g.surfaces satisfying aH + bK = 1, where a and b are positive. Duke Math. J.73, No 2, 291-306 ( 1994). Zbl0802.53002MR1262209
  86. [86] W. Rossman and K. Sato. Constant mean curvature surfaces in hyperbolic 3-space with two ends. J. Exp.Math., No 1,101-1197 ( 1998). Zbl0980.53081MR1677103
  87. [87] W. Rossman, M. Umehara and K. Yamada. Irreducible constant mean curvature l surfaces in hyperbolic space with positive genus. Tôhoku Math. J., 449-484, 49 ( 1997). Zbl0913.53025MR1478909
  88. [88] R. Sa Earp. Recent developments on the structure of compact surfaces with planar boundary In: The Problem of Plateau (edited by Th.M. Rassias), pp. 245-257, World Scientific ( 1992). Zbl0790.53008MR1209221
  89. [89] R. Sa Earp. On two mean curvature equations in hyperbolic space. In: New Approaches in Nonlinear Analysis (editedby Th.Rassias), Hadronic Press, U.S.A., 171-182 ( 1999). Zbl0960.53034
  90. [90] R. Sa Earp and E. Toubiana. Sur les surfaces de Weingarten spéciales de type minimal Boletim da Socie dade Brasileira deMatemática, 26, No. 2, 129-148 ( 1995). Zbl0864.53004MR1364263
  91. [91] R. Sa Earp and E. Toubiana. Classification des Surfaces Speciales de Revolution de Type Delaunay. Amer. J. Math. 121, No 3, 671-700 ( 1999). Zbl0972.53007MR1738404
  92. [92] R. Sa Earp and E. Toubiana. Symmetry of properly embedded special Weingarten surfacesin H3. Trans. Amer. Math. Soc. 352, No 12, 4693-4711 ( 1999). Zbl0989.53003MR1675186
  93. [93] R. Sa Earp and E. Toubiana. Some applications of maximum principle to hypersurfaces in Euclidean and hyperbolic space. In: New Approaches in Nonlinear Analysis (edited by Th.Rassias), Hadronic Press, U.S.A., 183-202 ( 1999). Zbl0959.53038
  94. [94] R. Sa Earp and E. Toubiana. Existence and uniqueness of minimal graphs in hyperbolic space. Asian Journal of Mathematics (new Journal), (Editors-in-Chief: S-T Yau (Harvard) e R. Chan (Hong Kong)),4, No. 3, 669-694, International Press ( 2000). Zbl0984.53005MR1796699
  95. [95] R. Sa Earp and E. Toubiana. On the Geometry of Constant Mean Curvature One Surfaces in Hyperbolic Space. Illinois J. Math. 45, No 2 ( 2001). Zbl0997.53042MR1878610
  96. [96] R. Sa Earp and E. Toubiana. Introduction à la géométrie hyperbolique et aux surfaces de Riemann. Diderot Editeur, Paris ( 1997). Zbl0944.30001
  97. [97] R. Sa Earp and E. Toubiana. Meromorphic data for mean curvature one surfaces in hyperbolic space. Preprint. Zbl1063.53010
  98. [98] R. Sa Earp and E. Toubiana. A Weierstrass-Kenmotsu formula for prescribed mean curvature surfaces in hyperbolic space. Séminaire de Théorie Spectrale et Géométrie de l'Institut Fourier de Grenoble, 19, 9-23 ( 2001). Zbl1014.53006MR1909073
  99. [99] R. Sa Earp and E. Toubiana. Meromorphic data for mean curvature one surfaces in hyperbolic space, II. Preprint. Zbl1063.53010
  100. [100] B. Semmler. Surfaces de courbure moyenne constante dans les espaces euclidien et hyperbolic, Docto Thesis, Univ. Paris VII, ( 1997). 
  101. [101] J. Serrin. A symmetry problem in potential theory. Arch. Rat. Mech. Anal. 43,304-318 ( 1971). Zbl0222.31007MR333220
  102. [102] R. Schoen. Uniqueness, symmetry, and embeddedness of minimal surfaces. J. Diff. Geom. 18, 791-809 ( 1983). Zbl0575.53037MR730928
  103. [103] M. SoretDéformations de surfaces minimales. Thèse de Doctorat, Univ. de Paris VII ( 1993). 
  104. [104] A.J. Small. Surfaces of constant mean curvature 1 in H3 and algebraic curves on a quadric. Proc. AMS 122 No4, 1211-1220 ( 1994). Zbl0823.53044MR1209429
  105. [105] B. Smyth. The generalization of Delaunay's theorem to constant mean curvature surfaces with conti nuous internai symmetry. Preprint. 
  106. [106] M. Spivak. A comprehensive introduction to differential geometry. Publish or Perish Volume IV, second edition ( 1979). Zbl0439.53004
  107. [107] K. Steffen. Parametric surfaces of prescribed mean curvature In: Calculus of variations and geometrie evolution problems (edited by S. Hildebrant and M. Struwe), 211-265, Lecture notes in Mathematics 1713, Springer ( 1999). Zbl0955.53033MR1731641
  108. [108] M. Struwe. Large H-surfaces via the Mountain-pass lemma. Math. Ann. 270, 441-459 ( 1985). Zbl0582.58010MR774369
  109. [109] M. Struwe. Plateau's problem and the calculus of variations. Math. Notes 35, Princeton Univ. Press ( 1989). Zbl0694.49028
  110. [110] M. Umehara and K. Yamada. Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space. Annals of Math. 137, 611-638 ( 1993). Zbl0795.53006MR1217349
  111. [111] M. Umehara and K. Yamada. A parametrization of the Weierstrass formulae and perturbation of some minimal surfaces in R3 into the hyperbolic 3-space. J. Reine Angew. Math. 432, 93-116 ( 1992). Zbl0757.53033MR1184761
  112. [112] M. Umehara and K. Yamada. Surfaces of constant mean curvature c in H3(-c2) with prescribed Gauss map. Math. Ann. 304, 203-224 ( 1996). Zbl0841.53050MR1371764
  113. [113] H. Wente. An existence theorem for surfaces of constant mean curvature. Math. Anal. Appl. 26, 318-344 ( 1969). Zbl0181.11501MR243467
  114. [114] H. Wente. A general existence theorem for surfaces of constant mean curvature. Math. Z. 120, 277-288 ( 1971). Zbl0214.11101MR282300
  115. [115] H. Wente. Large solutions to the volume constrained Plateau problem. Arch. Mech. Anal. 75, 59-77 ( 1980). Zbl0473.49029MR592104
  116. [116] H. Wente. A counter-example to the conjecture of H. Hopf. Pacific J. Math. 121,193-243 ( 1986). Zbl0586.53003
  117. [117] S.-T Yau. Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math. XXVIII, 201-228 ( 1975). Zbl0291.31002MR431040

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.