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A note on rigidity theorem of λ-hypersurfaces

Part of: Global differential geometry

Published online by Cambridge University Press:  18 January 2019

Guoxin Wei  and
Yejuan Peng
Guoxin Wei
Affiliation:
School of Mathematical Sciences, South China Normal University, 510631 Guangzhou, China ([email protected])
Yejuan Peng
Affiliation:
School of Mathematics and Information Sciences, Henan Normal University, 453007 Xinxiang, China ([email protected])
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Abstract

Self-shrinkers are an important class of solutions to the mean curvature flow and their generalization is λ-hypersurfaces. In this paper, we study λ-hypersurfaces and give a rigidity result about complete λ-hypersurfaces.

Keywords

mean curvaturethe weighted area functionalλ-hypersurfacesthe weighted volume-preserving mean curvature flow

MSC classification

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 6 , December 2019 , pp. 1595 - 1601
Copyright
Copyright © Royal Society of Edinburgh 2019 

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