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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A class of weighted isoperimetric inequalities in hyperbolic space
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by Haizhong Li and Botong Xu
Proc. Amer. Math. Soc. 151 (2023), 2155-2168
DOI: https://doi.org/10.1090/proc/16219
Published electronically: February 28, 2023

Abstract:

In this paper, we prove a class of weighted isoperimetric inequalities for bounded domains in hyperbolic space by using the isoperimetric inequality with log-convex density in Euclidean space. As a consequence, we remove the horo-convex assumption of domains in a weighted isoperimetric inequality proved by Scheuer-Xia [Trans. Amer. Math. Soc. 372 (2019), pp. 6771–6803]. Furthermore, we prove weighted isoperimetric inequalities for star-shaped domains in warped product manifolds. Particularly, we obtain a weighted isoperimetric inequality for star-shaped hypersurfaces lying outside a certain radial coordinate slice in the anti-de Sitter-Schwarzschild manifold.
References
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Bibliographic Information
  • Haizhong Li
  • Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
  • MR Author ID: 255846
  • Email: lihz@tsinghua.edu.cn
  • Botong Xu
  • Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
  • ORCID: 0000-0001-8878-0096
  • Email: xbt17@mails.tsinghua.edu.cn
  • Received by editor(s): March 25, 2022
  • Received by editor(s) in revised form: July 16, 2022
  • Published electronically: February 28, 2023
  • Additional Notes: The authors were supported by NSFC Grant No. 11831005 and NSFC Grant No. 12126405.
  • Communicated by: Gaoyong Zhang
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2155-2168
  • MSC (2020): Primary 52A40; Secondary 53C24
  • DOI: https://doi.org/10.1090/proc/16219
  • MathSciNet review: 4556208