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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Relating diameter and mean curvature for Riemannian submanifolds
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by Jia-Yong Wu and Yu Zheng PDF
Proc. Amer. Math. Soc. 139 (2011), 4097-4104 Request permission

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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Additional Information
  • Jia-Yong Wu
  • Affiliation: Department of Mathematics, Shanghai Maritime University, Haigang Avenue 1550, Shanghai 201306, People’s Republic of China
  • Email: jywu81@yahoo.com
  • Yu Zheng
  • Affiliation: Department of Mathematics, East China Normal University, Dong Chuan Road 500, Shanghai 200241, People’s Republic of China
  • MR Author ID: 337221
  • Email: zhyu@math.ecnu.edu.cn
  • Received by editor(s): January 24, 2010
  • Received by editor(s) in revised form: September 23, 2010
  • Published electronically: March 25, 2011
  • Additional Notes: This work is partially supported by NSFC10871069.
  • Communicated by: Michael Wolf
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 4097-4104
  • MSC (2010): Primary 53C40, Secondly, 57R42
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10848-7
  • MathSciNet review: 2823054