Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications
Compositio Mathematica, Volume 86 (1993) no. 3, pp. 317-335.
@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},
     pages = {317--335},
     publisher = {Kluwer Academic Publishers},
     volume = {86},
     number = {3},
     year = {1993},
     mrnumber = {1219631},
     zbl = {0782.53054},
     language = {en},
     url = {http://www.numdam.org/item/CM_1993__86_3_317_0/}
}
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
SP  - 317
EP  - 335
VL  - 86
IS  - 3
PB  - Kluwer Academic Publishers
UR  - http://www.numdam.org/item/CM_1993__86_3_317_0/
LA  - en
ID  - CM_1993__86_3_317_0
ER  - 
%0 Journal Article
%A Miquel, Vicente
%A Palmer, Vicente
%T Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications
%J Compositio Mathematica
%D 1993
%P 317-335
%V 86
%N 3
%I Kluwer Academic Publishers
%U http://www.numdam.org/item/CM_1993__86_3_317_0/
%G en
%F CM_1993__86_3_317_0
Miquel, Vicente; Palmer, Vicente. Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications. Compositio Mathematica, Volume 86 (1993) no. 3, pp. 317-335. http://www.numdam.org/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 | Zbl

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

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

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

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

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

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

[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

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

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