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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the heat kernel comparison theorems for minimal submanifolds


Author: Steen Markvorsen
Journal: Proc. Amer. Math. Soc. 97 (1986), 479-482
MSC: Primary 58G11; Secondary 53C42
MathSciNet review: 840633
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0840633-4
PII: S 0002-9939(1986)0840633-4
Article copyright: © Copyright 1986 American Mathematical Society