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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An Obata-type formula and the Liouville-type theorem for a class of K-Hessian equations on the sphere
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by Shujun Shi, Peihe Wang, Tian Wu and Hua Zhu;
Proc. Amer. Math. Soc. 152 (2024), 3537-3550
DOI: https://doi.org/10.1090/proc/16857
Published electronically: June 21, 2024

Abstract:

In this paper, we study a class of $k$-Hessian equations, we can deduce an Obata-type formula and a Liouville-type theorem by integration by parts.
References
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Bibliographic Information
  • Shujun Shi
  • Affiliation: School of Mathematical Sciences, Harbin Normal University, Harbin 150025, HeiLongjiang PROVINCE, People’s Republic of China
  • ORCID: 0000-0002-3880-7884
  • Email: shjshi@hrbnu.edu.cn
  • Peihe Wang
  • Affiliation: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ShanDong PROVINCE, People’s Republic of China
  • Email: peihewang@hotmail.com
  • Tian Wu
  • Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, AnHui PROVINCE, People’s Republic of China
  • Email: wt1997@mail.ustc.edu.cn
  • Hua Zhu
  • Affiliation: School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, SiChuan PROVINCE, People’s Republic of China; \normalfont and School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, AnHui PROVINCE, People’s Republic of China
  • ORCID: 0009-0003-1002-0240
  • Email: zhuhmaths@mail.ustc.edu.cn
  • Received by editor(s): September 18, 2023
  • Received by editor(s) in revised form: January 8, 2024, March 1, 2024, and March 2, 2024
  • Published electronically: June 21, 2024
  • Additional Notes: The first author was supported by the National Natural Science Foundation of China under Grant 11971137. The fourth author was supported by the National Natural Science Foundation of China under Grant 12301098.
  • Communicated by: Jiaping Wang
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3537-3550
  • MSC (2020): Primary 35J60; Secondary 35B45
  • DOI: https://doi.org/10.1090/proc/16857
  • MathSciNet review: 4767282