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arXiv · 1001.3463

Relating diameter and mean curvature for Riemannian submanifolds

Jia-Yong Wu·Yu Zheng
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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 Topping in the Euclidean case (Comment. Math. Helv., 83 (2008), 539--546).

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Jia-Yong Wu, Yu Zheng. 2010-10-20. Relating diameter and mean curvature for Riemannian submanifolds. https://arxiv.org/abs/1001.3463

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