On the heat kernel comparison theorems for minimal submanifolds-Reference-Cited by-同舟云学术

On the heat kernel comparison theorems for minimal submanifolds

Published:1986 Issue:3 Volume:97 Page:479-482
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Markvorsen Steen

Abstract

In [3], Cheng, Li and Yau proved comparison theorems (upper bounds) for the heat kernels on minimal submanifolds of space forms. In the present note we show that these comparison theorems together with a series of corollaries remain true for minimal submanifolds in ambient spaces with just an upper bound on the sectional curvature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1986-097-03/S0002-9939-1986-0840633-4/S0002-9939-1986-0840633-4.pdf

Reference4 articles.

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

2. On the total curvature of immersed manifolds. II. Mean curvature and length of second fundamental form;Chen, Bang-yen;Amer. J. Math.,1972

3. Heat equations on minimal submanifolds and their applications;Cheng, Shiu Yuen;Amer. J. Math.,1984

4. S. Markvorsen, On the bass note of compact minimal immersions, Preprint MPI, Bonn, 1985.

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