Neumann eigenvalue estimate on a compact Riemannian manifold
Author:
Roger Chen
Journal:
Proc. Amer. Math. Soc. 108 (1990), 961-970
MSC:
Primary 58G25; Secondary 35P15
DOI:
https://doi.org/10.1090/S0002-9939-1990-0993745-X
MathSciNet review:
993745
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In their article, P. Li and S. T. Yau give a lower bound of the first Neumann eigenvalue in terms of geometrical invariants for a compact Riemannian manifold with convex boundary. The purpose of this paper is to generalize their result to a compact Riemannian manifold with possibly nonconvex boundary.
- [1] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problem in Analysis, Princeton Univ. Press, Princeton, NJ, 1970, pp. 195-199. MR 0402831 (53:6645)
- [2] P. Li and S. T. Yau, Estimates of eigenvalues of a compact Riemannian manifold, Proc. Sympos. Pure Math., vol. 36, Amer. Math. Soc., Providence, RI, 1980, pp. 205-240. MR 573435 (81i:58050)
- [3] L. E. Payne and I. Stakgold, On the mean value of the fundamental mode in the fixed membrane problem. Applicable Anal. 3 (1973), 295-303. MR 0399633 (53:3476)
- [4] L. E. Payne and H. Weinberger, The optimal Poincaré inequality for convex domains, Arch. Rational Mech. Anal. 5 (1960), 282-292. MR 0117419 (22:8198)
- [5] F. W. Warner, Extension of the Rauch comparison theorem to submanifolds, Trans. Amer. Math. Soc. 122 (1966), 341-356. MR 0200873 (34:759)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G25, 35P15
Retrieve articles in all journals with MSC: 58G25, 35P15
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-0993745-X
Article copyright:
© Copyright 1990
American Mathematical Society
