On the heat kernel comparison theorems for minimal submanifolds
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- by Steen Markvorsen PDF
- Proc. Amer. Math. Soc. 97 (1986), 479-482 Request permission
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.References
- Jeff Cheeger and Shing Tung Yau, A lower bound for the heat kernel, Comm. Pure Appl. Math. 34 (1981), no. 4, 465–480. MR 615626, DOI 10.1002/cpa.3160340404
- Bang-yen Chen, On the total curvature of immersed manifolds. II. Mean curvature and length of second fundamental form, Amer. J. Math. 94 (1972), 799–809. MR 319114, DOI 10.2307/2373759
- Shiu Yuen Cheng, Peter Li, and Shing-Tung Yau, Heat equations on minimal submanifolds and their applications, Amer. J. Math. 106 (1984), no. 5, 1033–1065. MR 761578, DOI 10.2307/2374272 S. Markvorsen, On the bass note of compact minimal immersions, Preprint MPI, Bonn, 1985.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 479-482
- MSC: Primary 58G11; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1986-0840633-4
- MathSciNet review: 840633