Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications
Miquel, Vicente ; Palmer, Vicente
Compositio Mathematica, Tome 89 (1993), p. 317-335 / Harvested from Numdam
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Publié le : 1993-01-01
@article{CM_1993__86_3_317_0,
     author = {Miquel, Vicente and Palmer, Vicente},
     title = {Mean curvature comparison for tubular hypersurfaces in K\"ahler manifolds and some applications},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {317-335},
     mrnumber = {1219631},
     zbl = {0782.53054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__86_3_317_0}
}

Miquel, Vicente; Palmer, Vicente. Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications. Compositio Mathematica, Tome 89 (1993) pp. 317-335. http://gdmltest.u-ga.fr/item/CM_1993__86_3_317_0/

[Bo] W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, New York, 1986. | MR 861409 | Zbl 0596.53001

[BC] R.L. Bishop and R.H. Crittenden, Geometry of manifolds, Academic Press, New York, 1964. | MR 169148 | Zbl 0132.16003

[Cg] S.Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289-297. | MR 378001 | Zbl 0329.53035

[Ch] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984. | MR 768584 | Zbl 0551.53001

[CV] B.Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Angew. Math. 325 (1981), 28-67. | MR 618545 | Zbl 0503.53013

[CY] J. Cheeger and S.T. Yau, A lower bound for the heat kernel, Comm. Pure Appl. Math. 34 (1981), 465-480. | MR 615626 | Zbl 0481.35003

[Dy] E.B. Dynkin, Markov processes, Springer Verlag, 1965. | Zbl 0132.37901

[EH] J.H. Eschenburg and E. Heintze, Comparison theory for Riccati equations, Manuscripta Math. 68 (1990), 209-215. | MR 1063226 | Zbl 0714.53029

[Ga] M. Gage, Upper bounds for the first eigenvalue of the Laplace-Beltrami operator, Indiana Univ. Math. J. 29 (1980), 897-912. | MR 589652 | Zbl 0465.53031

[Gi1] F. Giménez, Comparison theorems for the volume of a complex submanifold of a Kähler manifold, Israel J. Math. 71 (1990), 239-255. | MR 1088818 | Zbl 0731.53062

[Gi2] F. Giménez, Teoremas de comparacin en variedades Kählerianas," Tesis Doctoral. Departamento de Geometria y Topologia. Universidad de Valencia, 1990.

[Gr1] A. Gray, Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula, Topology 21 (1982), 201-228. | MR 642000 | Zbl 0487.53035

[Gr2] A. Gray, Volumes of tubes about complex submanifolds of complex projective space, Trans. Amer. Math. Soc. 291 (1985), 437-449. | MR 800247 | Zbl 0575.53043

[Gr3] A. Gray, Tubes, Addison-Wesley, Reading, 1990. | MR 1044996 | Zbl 0692.53001

[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. | MR 830234 | Zbl 0593.58047

[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. | MR 1038727 | Zbl 0728.53034

[GM2] F. Giménez and V. Miquel, Bounds for the first Dirichlet eigenvalue of domains in Kähler manifolds, Archiv der Math. 56 (1991), 370-375. | MR 1094424 | Zbl 0735.58009

[GW] R.E. Greene and H. Wu, C∞ approximations of convex, subharmonic and plurisubharmonic functions, Ann. Sci. Ec. Nor. Sup. 12 (1979), 47-84. | Numdam | Zbl 0415.31001

[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. | Numdam | MR 533065 | Zbl 0416.53027

[Ka] H. Karcher, Riemannian comparison constructions, in, Global Differential Geometry, edited by S. S. Chern, M.A.A., 1989, 170-222. | MR 1013810 | Zbl 0683.53040

[Ki] M. Kimura, Real Hypersurfaces and complex manifolds in complex projective space, Trans. Am. Math. Soc. 296 (1986), 137-149. | MR 837803 | Zbl 0597.53021

[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. | Numdam | MR 744066 | Zbl 0553.53026

[K-N] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience, New York, 1969.

[Le] J.M. Lee, Eigenvalue comparison for tubular domains, Proc. Am. Math. Soc. 109 (1990), 843-848. | MR 1021900 | Zbl 0702.58076

[Ma] S.M. Markvorsen, On the heat kernel comparison theorems for minimal submanifolds, Proc. Amer. Math. Soc. 97 (1986), 479-482. | MR 840633 | Zbl 0597.53049

[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. | MR 1172621 | Zbl 0773.53027

[Na] S. Nayatani, On the volume of positively curved Kähler manifolds, Osaka J. Math. 25 (1988), 223-231. | MR 937197 | Zbl 0647.53050

[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. | MR 1161810

[Ro] H.L. Royden, Comparison Theorems for the Matrix Riccati Equation, Comm. on Pure and Applied Math. 41 (1988), 739-746. | MR 948079 | Zbl 0632.34028

[Sz] Z.I. Szabó, The Lichnerowicz conjecture on Harmonic manifolds, J. Differential Geom. 31 (1990), 1-28. | MR 1030663 | Zbl 0686.53042