Existence results for embedded minimal surfaces of controlled topological type, I

Jürgen Jost

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 1, page 15-50
  • ISSN: 0391-173X

How to cite

top

Jost, Jürgen. "Existence results for embedded minimal surfaces of controlled topological type, I." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.1 (1986): 15-50. <http://eudml.org/doc/83972>.

@article{Jost1986,
author = {Jost, Jürgen},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {embedded minimal surfaces of controlled topological type; boundary regularity; fixed and free boundaries; Riemannian manifolds},
language = {eng},
number = {1},
pages = {15-50},
publisher = {Scuola normale superiore},
title = {Existence results for embedded minimal surfaces of controlled topological type, I},
url = {http://eudml.org/doc/83972},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Jost, Jürgen
TI - Existence results for embedded minimal surfaces of controlled topological type, I
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 1
SP - 15
EP - 50
LA - eng
KW - embedded minimal surfaces of controlled topological type; boundary regularity; fixed and free boundaries; Riemannian manifolds
UR - http://eudml.org/doc/83972
ER -

References

top
  1. [AW1] W. Allard, On the first variation of a varifold, Ann. of Math., 95 (1972), pp. 417-491. Zbl0252.49028MR307015
  2. [AW2] W. Allard, On the first variation of a varifold boundary behaviour, Ann.. of Math.101 (1975), pp. 418-446. Zbl0319.49026MR397520
  3. [AA] W. Allard - F. Almgren, Jr., The structure of stationary one dimensional dimensional varifolds with positive density, Inv. Math., 34 (1976), pp. 83-97., Zbl0339.49020MR425741
  4. [A] F. Almgren, Jr., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and and singularity structure, Ann. of Math., 87 (1968), pp. 321-391. Zbl0162.24703MR225243
  5. [AS] F. Almgren, Jr. - L. Simon, Existence of embedde solutions of Plateau's problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 6 (1979), pp. 447-495. Zbl0417.49051MR553794
  6. [A1] H.W. Alt, Verzweigungspunkte von H - Flächen I, Math. Z., 127 (1972), pp. 333-362. Zbl0253.58007MR312404
  7. [A2] H W., ALT, Verzweigungspunkte von H - Flächen II, Math. Ann., 101 (1973), pp. 33-55. Zbl0257.58005MR331195
  8. [FHS] M. Freedman - J. Hass - P. Scott, Least area incompressible surface in 3-manifolds, Inv. Math., 71 (1983), pp. 609-642. Zbl0482.53045MR695910
  9. [GHN] M. Grüter - S. Hildebrandt - J.C.C. Nitsche, On the boundary behaviour of minimal surfaces with a free boundary which are not minima of the area, Manuscripta Math., 35 (1981), pp. 387-410. Zbl0483.49037MR636464
  10. [GJ1] M. Grüter - J. Jost, Allard type regularity results for varifolds with free boundaries, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), to appear. Zbl0615.49018MR863638
  11. [GJ2] M. Grüter - J. Jost, On embedded minimal disks in convex bodies, Anal. nonlinéaire, to appear. Zbl0617.49017MR868522
  12. [Gu] R. Gulliver, Regularity of minimizing surfaces of prescribed mean curvature, Ann. Math.97 (1973), 275-305. Zbl0246.53053MR317188
  13. [GS] R. Gulliver - J. Spruck, On embedded minimal surfaces, Ann. Math., 103 (1976), pp. 331-347, Correction in Ann. Math., 109 (1979), pp. 407-412. Zbl0347.49033MR405217
  14. [HS] R. Hardt - L. Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. Math., 110 (1979), pp. 439-486. Zbl0457.49029MR554379
  15. [HH] E. Heinz - S. Hildebrandt, Remarks on minimal surfaces in Riemannian manifolds, CPAM, 23 (1970), pp. 371-377. Zbl0188.42102MR259765
  16. [Hi] S. Hildebrandt, Boundary behavior of minimal surfaces, Arch. Rational Mech. Anal., 35 (1969), pp. 47-82. Zbl0183.39402MR248650
  17. [HN] S. Hildebrandt - J.C.C. Nitche, Geometric properties of minimal surfaces with free boundaries, SFB 72, Preprint 527, Bonn, 1982. 
  18. [J1] J. Jost, Harmonic maps between surfaces, Springer, Lecture Notes in Math., 1062 (1984). Zbl0542.58002MR754769
  19. [J2] J. Jost, Conformal mappings and the Plateau-Douglas problem, J. reine angew. Math., 359 (1985), pp. 37-54. Zbl0568.49025MR794798
  20. [JK] J. Jost - H. Karcher, Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen, Manuscripta Math., 40 (1982), pp. 27-77. Zbl0502.53036MR679120
  21. [KÜ] A. Küster, The optimal version of Hildebrand's and Nitsche's estimate of the length of the trace of a minimal surface with a partially free boundary, SFB 72, Preprint 577, Bonn, 1983. 
  22. [MSY] W. MeeksIII - L. Simon - S.T. Yau, Embedded minumal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. Math., 116 (1982), pp. 621-659. Zbl0521.53007MR678484
  23. [MY1] W. MeeksIII - S.T. Yau, The classical Plateau problem and the topology of three-dimensional manifolds, Top.21 (1982), pp. 409-442. Zbl0489.57002MR670745
  24. [MY2] W. MeeksIII - S.T. Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory, Ann. Math., 112 (1980), pp. 441-484. Zbl0458.57007MR595203
  25. [MY3] W. MeeksIII - S.T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z., 179 (1982), pp. 151-168. Zbl0479.49026MR645492
  26. [Mu] D. Mumford, A remark on Mahler's compactness theorem, Proc. AMS29 (1971), pp. 289-294. Zbl0215.23202MR276410
  27. [N] J.C.C. Nitsche, Vorlesungen über Minimalflächen, Springer, 1975. Zbl0319.53003MR448224
  28. [O] R. Osserman, A proof of the regularity everywhere of the classical solution of Plateau's problem, Ann. Math.91 (1970), pp. 550-569. Zbl0194.22302MR266070
  29. [P] J. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Math. Notes 27, Princeton Univ. Press, 1981. Zbl0462.58003MR626027
  30. [SY] R. Schoen - S.T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with nonnegative scalar curvature, Ann. Math.110 (1979), pp. 127-142. Zbl0431.53051MR541332
  31. [SS] L. Simon - F. Smith, On the existence of embedded minimal 2-spheres in the 3-sphere, endowed with an arbitrary metric, to appear. 
  32. [TJ] J. Taylor, Boundary regularity for solutions to various capillarity and free boundary problems, Comm. PDE, 2 (1977), pp. 323-357. Zbl0357.35010MR487721
  33. [Td] P. Tolksdorf, A parametric variational principle for minimal surfaces of varying topological type, SFB 72, Preprint 621, Bonn, 1983. MR767571
  34. [TT1] F. Tomi - A. Tromba, Extrem curves bound embedded minimal surfaces of the type of the disc, Math. Z., 158 (1978), pp. 137-145. Zbl0353.53032MR486522
  35. [TT2] F. Tomi - A. Tromba, On Plateau's problem for minimal surfaces of higher genus in R3, Bull. AMS, 13 (1985), pp. 169-171. Zbl0589.49026MR799805

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.