Communications in Analysis and Geometry

Volume 30 (2022)

Number 5

Stability and area growth of $\lambda$-hypersurfaces

Pages: 1059 – 1091

DOI: https://dx.doi.org/10.4310/CAG.2022.v30.n5.a4

Authors

Qing-Ming Cheng (Department of Applied Mathematics, Faculty of Sciences, Fukuoka University, Fukuoka, Japan)

Guoxin Wei (School of Mathematical Sciences, South China Normal University, Guangzhou, China)

Abstract

In this paper, We define a $\mathcal{F}$-functional and study $\mathcal{F}$-stability of $\lambda$-hypersurfaces, which extend a result of Colding–Minicozzi [6]. Lower bound growth and upper bound growth of area for complete and non-compact $\lambda$-hypersurfaces are studied.

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The first author was partially supported by JSPS Grant-in-Aid for Scientific Research (B): No.16H03937

The second author was partly supported by NSFC Grant No.11771154, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2018), Guangdong Natural Science Foundation Grant No.2019A1515011451.

Received 26 December 2015

Accepted 30 October 2019

Published 17 March 2023