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Superconvexity of the heat kernel on hyperbolic space with applications to mean curvature flow

Zhang, Yongzhe (2021) Superconvexity of the heat kernel on hyperbolic space with applications to mean curvature flow. Proceedings of the American Mathematical Society, 149 (5). pp. 2161-2166. ISSN 0002-9939. doi:10.1090/proc/15379. https://resolver.caltech.edu/CaltechAUTHORS:20210506-153612783

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Abstract

We prove a conjecture of Bernstein that the heat kernel on hyperbolic space of any dimension is supercovex in a suitable coordinate and, hence, there is an analog of Huisken's monotonicity formula for mean curvature flow in hyperbolic space of all dimensions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/proc/15379DOIArticle
https://arxiv.org/abs/2008.11240arXivDiscussion Paper
Alternate Title:Superconvexity of the Heat Kernel on Hyperbolic Space
Additional Information:© 2021 American Mathematical Society. The author was partially supported by the NSF grants DMS-2018220 and DMS-2018221. The author would like to thank Professor Lu Wang for suggesting this question and her continuous guidance. Also, the author is grateful to the anonymous referees for their useful comments.
Funders:
Funding AgencyGrant Number
NSFDMS-2018220
NSFDMS-2018221
Subject Keywords:Superconvexity, heat kernel, hyperbolic space, mean curvature flow
Issue or Number:5
Classification Code:2020 Mathematics Subject Classification: Primary 35K08, 58J35; Secondary 35K93
DOI:10.1090/proc/15379
Record Number:CaltechAUTHORS:20210506-153612783
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210506-153612783
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108997
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 May 2021 22:54
Last Modified:06 May 2021 22:54

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