Relating diameter and mean curvature for Riemannian submanifolds
Differential Geometry
2010-10-21 v2
Abstract
Given an -dimensional closed connected Riemannian manifold smoothly isometrically immersed in an -dimensional Riemannian manifold , we estimate the diameter of in terms of its mean curvature field integral under some geometric restrictions, and therefore generalize a recent work of Topping in the Euclidean case (Comment. Math. Helv., 83 (2008), 539--546).
Cite
@article{arxiv.1001.3463,
title = {Relating diameter and mean curvature for Riemannian submanifolds},
author = {Jia-Yong Wu and Yu Zheng},
journal= {arXiv preprint arXiv:1001.3463},
year = {2010}
}
Comments
8 pages; typos corrected, references added, several explanations also added; to appear in in Proc. Amer. Math. Soc