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Willmore inequality on hypersurfaces in hyperbolic space


Author: Yingxiang Hu
Journal: Proc. Amer. Math. Soc. 146 (2018), 2679-2688
MSC (2010): Primary 53C42, 53C44
DOI: https://doi.org/10.1090/proc/13968
Published electronically: February 1, 2018
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Abstract: In this article, we prove a geometric inequality for star-shaped and mean-convex hypersurfaces in hyperbolic space by inverse mean curvature flow. This inequality can be considered as a generalization of Willmore inequality for a closed surface in hyperbolic $ 3$-space.


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Yingxiang Hu
Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Beijing 100086, People’s Republic of China
Email: huyingxiang10@163.com

DOI: https://doi.org/10.1090/proc/13968
Keywords: Willmore inequality, inverse curvature flow, hyperbolic space
Received by editor(s): November 27, 2016
Received by editor(s) in revised form: September 13, 2017
Published electronically: February 1, 2018
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society

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