Comparison formulas for total mean curvatures of Riemannian hypersurfaces-Reference-Cited by-同舟云学术

Comparison formulas for total mean curvatures of Riemannian hypersurfaces

Published:2024-02-01 Issue:1 Volume:24 Page:97-102
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Ghomi Mohammad¹

Affiliation:

1. School of Mathematics , Georgia Institute of Technology , Atlanta , GA 30332 , USA

Abstract

Abstract We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel Spruck, which had been obtained via Reilly’s identities.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0081/pdf

Reference7 articles.

1. M. Ghomi and J. Spruck, “Total mean curvatures of Riemannian hypersurfaces,” Adv. Nonlinear Stud., vol. 23, no. 1, p. 20220029, 2023. https://doi.org/10.1515/ans-2022-0029.

2. M. Ghomi and J. Spruck, “Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds,” J. Geom. Anal., vol. 32, no. 2, p. 54, 2022. https://doi.org/10.1007/s12220-021-00801-2.

3. R. C. Reilly, “Applications of the hessian operator in a riemannian manifold,” Indiana Univ. Math. J., vol. 26, no. 3, pp. 459–472, 1977. https://doi.org/10.1512/iumj.1977.26.26036.

4. S.-s. Chern, “On the curvatura integra in a Riemannian manifold,” Ann. Math., vol. 46, no. 2, pp. 674–684, 1945. https://doi.org/10.2307/1969203.

5. A. Borbély, “An estimate for the total mean curvature in negatively curved spaces,” Bull. Aust. Math. Soc., vol. 66, no. 2, pp. 267–273, 2002. https://doi.org/10.1017/s0004972700040119.