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Eigenvalue comparison for tubular domains


Author: Jeffrey M. Lee
Journal: Proc. Amer. Math. Soc. 109 (1990), 843-848
MSC: Primary 58G20; Secondary 35P15, 53C40, 58G30
DOI: https://doi.org/10.1090/S0002-9939-1990-1021900-1
MathSciNet review: 1021900
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Abstract: S. Y. Cheng's eigenvalue comparison theorem for geodesic balls is generalized to certain tubular domains. This gives application to the infinitesimal volume comparison theory developed by E. Heintze and H. Karcher as well as A. Gray.


References [Enhancements On Off] (What's this?)

  • [C] S.-Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289-297. MR 0378001 (51:14170)
  • [Gr] A. Gray, Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula, Topology 21 (1982), 201-228. MR 642000 (83c:53064)
  • [H-K] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. Ecole Norm. Sup. 11 (1978), 451-470. MR 533065 (80i:53026)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1021900-1
Keywords: Laplace operator, Riemannian manifold, eigenvalues, tubular domain, spectral geometry
Article copyright: © Copyright 1990 American Mathematical Society

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