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Proceedings of the American Mathematical Society

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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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  • [1] J. Cheeger and S.-T. Yau, A lower bound for the heat kernel, Comm. Pure Appl. Math. 34 (1981), 465-480. MR 615626 (82i:58065)
  • [2] B.-Y. Chen, On the total curvature of immersed manifolds. II, Amer. J. Math. 94 (1972), 799-809. MR 0319114 (47:7660)
  • [3] S.-Y. Cheng, P. Li and S.-T. Yau, Heat equations on minimal submanifolds and their applications, Amer. J. Math. 106 (1984), 1033-1065. MR 761578 (85m:58171)
  • [4] S. Markvorsen, On the bass note of compact minimal immersions, Preprint MPI, Bonn, 1985.

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Article copyright: © Copyright 1986 American Mathematical Society

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