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
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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