Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications

Vicente Miquel; Vicente Palmer

Compositio Mathematica (1993)

  • Volume: 86, Issue: 3, page 317-335
  • ISSN: 0010-437X

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Miquel, Vicente, and Palmer, Vicente. "Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications." Compositio Mathematica 86.3 (1993): 317-335. <http://eudml.org/doc/90224>.

@article{Miquel1993,
author = {Miquel, Vicente, Palmer, Vicente},
journal = {Compositio Mathematica},
keywords = {sectional curvatures; Jacobi operator; totally geodesic; unit Hopf bundle; mean curvatures; first Dirichlet eigenvalue; mean exit time},
language = {eng},
number = {3},
pages = {317-335},
publisher = {Kluwer Academic Publishers},
title = {Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications},
url = {http://eudml.org/doc/90224},
volume = {86},
year = {1993},
}

TY - JOUR
AU - Miquel, Vicente
AU - Palmer, Vicente
TI - Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 86
IS - 3
SP - 317
EP - 335
LA - eng
KW - sectional curvatures; Jacobi operator; totally geodesic; unit Hopf bundle; mean curvatures; first Dirichlet eigenvalue; mean exit time
UR - http://eudml.org/doc/90224
ER -

References

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  1. [Bo] W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, New York, 1986. Zbl0596.53001MR861409
  2. [BC] R.L. Bishop and R.H. Crittenden, Geometry of manifolds, Academic Press, New York, 1964. Zbl0132.16003MR169148
  3. [Cg] S.Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z.143 (1975), 289-297. Zbl0329.53035MR378001
  4. [Ch] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984. Zbl0551.53001MR768584
  5. [CV] B.Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Angew. Math.325 (1981), 28-67. Zbl0503.53013MR618545
  6. [CY] J. Cheeger and S.T. Yau, A lower bound for the heat kernel, Comm. Pure Appl. Math.34 (1981), 465-480. Zbl0481.35003MR615626
  7. [Dy] E.B. Dynkin, Markov processes, Springer Verlag, 1965. Zbl0132.37901
  8. [EH] J.H. Eschenburg and E. Heintze, Comparison theory for Riccati equations, Manuscripta Math.68 (1990), 209-215. Zbl0714.53029MR1063226
  9. [Ga] M. Gage, Upper bounds for the first eigenvalue of the Laplace-Beltrami operator, Indiana Univ. Math. J.29 (1980), 897-912. Zbl0465.53031MR589652
  10. [Gi1] F. Giménez, Comparison theorems for the volume of a complex submanifold of a Kähler manifold, Israel J. Math.71 (1990), 239-255. Zbl0731.53062MR1088818
  11. [Gi2] F. Giménez, Teoremas de comparacin en variedades Kählerianas," Tesis Doctoral. Departamento de Geometria y Topologia. Universidad de Valencia, 1990. 
  12. [Gr1] A. Gray, Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula, Topology21 (1982), 201-228. Zbl0487.53035MR642000
  13. [Gr2] A. Gray, Volumes of tubes about complex submanifolds of complex projective space, Trans. Amer. Math. Soc.291 (1985), 437-449. Zbl0575.53043MR800247
  14. [Gr3] A. Gray, Tubes, Addison-Wesley, Reading, 1990. Zbl0692.53001MR1044996
  15. [GKP] A. Gray, L. Karp and M.A. Pinsky, The Mean Exit Time from a Tube in a Riemannian Manifold, in (1986), Probability Theory and Harmonic Analysis, edited by J. A. Chao and W. A. Woyczyński, Marcel Dekker, New York. Zbl0593.58047MR830234
  16. [GM1] F. Giménez and V. Miquel, Volume estimates for real hypersurfaces of a Kähler manifold with strictly positive holomorphic sectional and antiholomorphic Ricci curvatures, Pacific J. Math.142 (1990), 23-39. Zbl0728.53034MR1038727
  17. [GM2] F. Giménez and V. Miquel, Bounds for the first Dirichlet eigenvalue of domains in Kähler manifolds, Archiv der Math.56 (1991), 370-375. Zbl0735.58009MR1094424
  18. [GW] R.E. Greene and H. Wu, C∞ approximations of convex, subharmonic and plurisubharmonic functions, Ann. Sci. Ec. Nor. Sup.12 (1979), 47-84. Zbl0415.31001
  19. [HK] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. Ec. Nor. Sup.11 (1978), 451-470. Zbl0416.53027MR533065
  20. [Ka] H. Karcher, Riemannian comparison constructions, in, Global Differential Geometry, edited by S. S. Chern, M.A.A., 1989, 170-222. Zbl0683.53040MR1013810
  21. [Ki] M. Kimura, Real Hypersurfaces and complex manifolds in complex projective space, Trans. Am. Math. Soc.296 (1986), 137-149. Zbl0597.53021MR837803
  22. [Ks] A. Kasue, On a lower bound for the first eigenvalue of the Laplace operator on a Riemannian manifold, Ann. Sci. Ec. Norm. Sup.17 (1984), 31-44. Zbl0553.53026MR744066
  23. [K-N] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience, New York, 1969. Zbl0175.48504
  24. [Le] J.M. Lee, Eigenvalue comparison for tubular domains, Proc. Am. Math. Soc.109 (1990), 843-848. Zbl0702.58076MR1021900
  25. [Ma] S.M. Markvorsen, On the heat kernel comparison theorems for minimal submanifolds, Proc. Amer. Math. Soc.97 (1986), 479-482. Zbl0597.53049MR840633
  26. [MP] V. Miquel and V. Palmer, A comparison theorem for the mean exit time from a domain in a Kähler manifold, Ann. Global Anal. Geom, 10 (1992) 73-80. Zbl0773.53027MR1172621
  27. [Na] S. Nayatani, On the volume of positively curved Kähler manifolds, Osaka J. Math.25 (1988), 223-231. Zbl0647.53050MR937197
  28. [Pa] V. Palmer, Un teorema de comparación para el tiempo de salida medio de una bola geodésica en una variedad Kähler, XV Jornadas Luso-espanholas de Matemática (1990) III, 173-178. MR1161810
  29. [Ro] H.L. Royden, Comparison Theorems for the Matrix Riccati Equation, Comm. on Pure and Applied Math.41 (1988), 739-746. Zbl0632.34028MR948079
  30. [Sz] Z.I. Szabó, The Lichnerowicz conjecture on Harmonic manifolds, J. Differential Geom.31 (1990), 1-28. Zbl0686.53042MR1030663

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