Relating diameter and mean curvature for Riemannian submanifolds

Jia Yong Wu; Yu Zheng

doi:10.1090/S0002-9939-2011-10848-7

Relating diameter and mean curvature for Riemannian submanifolds

Jia Yong Wu^*
, Yu Zheng

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai Maritime University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Given an m-dimensional closed connected Riemannian manifold M smoothly isometrically immersed in an n-dimensional Riemannian manifold N, we estimate the diameter of M in terms of its mean curvature field integral under some geometric restrictions, and therefore generalize a recent work of P. M. Topping in the Euclidean case (Comment. Math. Helv., 83 (2008), 539-546).

Original language	English
Pages (from-to)	4097-4104
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2011-10848-7
State	Published - Nov 2011

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title = "Relating diameter and mean curvature for Riemannian submanifolds",

abstract = "Given an m-dimensional closed connected Riemannian manifold M smoothly isometrically immersed in an n-dimensional Riemannian manifold N, we estimate the diameter of M in terms of its mean curvature field integral under some geometric restrictions, and therefore generalize a recent work of P. M. Topping in the Euclidean case (Comment. Math. Helv., 83 (2008), 539-546).",

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AU - Zheng, Yu

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AB - Given an m-dimensional closed connected Riemannian manifold M smoothly isometrically immersed in an n-dimensional Riemannian manifold N, we estimate the diameter of M in terms of its mean curvature field integral under some geometric restrictions, and therefore generalize a recent work of P. M. Topping in the Euclidean case (Comment. Math. Helv., 83 (2008), 539-546).

UR - https://www.scopus.com/pages/publications/79960752567

U2 - 10.1090/S0002-9939-2011-10848-7

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M3 - 文章

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VL - 139

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

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Relating diameter and mean curvature for Riemannian submanifolds

Abstract

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