Relating diameter and mean curvature for Riemannian submanifolds
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- by Jia-Yong Wu and Yu Zheng PDF
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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 P. M. Topping in the Euclidean case (Comment. Math. Helv., 83 (2008), 539–546).References
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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