Exponential growth and the spectrum of the Laplacian

Author:

Brooks Robert

Abstract

Conditions are given on a noncompact manifold which allow one to conclude that 0 is in the spectrum of the Laplacian on M M .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. The fundamental group and the spectrum of the Laplacian;Brooks, Robert;Comment. Math. Helv.,1981

2. A lower bound for the heat kernel;Cheeger, Jeff;Comm. Pure Appl. Math.,1981

3. Differential equations on Riemannian manifolds and their geometric applications;Cheng, S. Y.;Comm. Pure Appl. Math.,1975

4. Asymptotic expansions for the compact quotients of properly discontinuous group actions;Donnelly, Harold;Illinois J. Math.,1979

5. \bysame, Stability theorems for the continuous spectrum of a negatively curved manifold (preprint).

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2. On the entropies of hypersurfaces with bounded mean curvature;Mathematische Annalen;2015-06-23

3. Curvature estimate for the volume growth of globally minimal submanifolds;Mathematische Annalen;1993-12

4. A relation between growth and the spectrum of the Laplacian;Mathematische Zeitschrift;1981-12

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