数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1405-1416.doi: 10.1007/s10473-021-0501-x

• 论文 •    下一篇

THE UNIQUENESS OF THE Lp MINKOWSKI PROBLEM FOR q-TORSIONAL RIGIDITY

孙广玲, 徐露, 章萍   

  1. School of Mathematics, Hunan University, Changsha 410082, China
  • 收稿日期:2020-08-19 修回日期:2021-04-14 出版日期:2021-10-25 发布日期:2021-10-21
  • 通讯作者: Lu XU E-mail:xulu@hnu.edu.cn
  • 作者简介:Guangling SUN,E-mail:sgl275869080@hnu.edu.cn;Ping ZHANG,E-mail:zping071727@hnu.edu.cn
  • 基金资助:
    The authors were supported by NSFC (11771132) and Hunan Science and Technology Project (2018JJ1004).

THE UNIQUENESS OF THE Lp MINKOWSKI PROBLEM FOR q-TORSIONAL RIGIDITY

Guangling SUN, Lu XU, Ping ZHANG   

  1. School of Mathematics, Hunan University, Changsha 410082, China
  • Received:2020-08-19 Revised:2021-04-14 Online:2021-10-25 Published:2021-10-21
  • Contact: Lu XU E-mail:xulu@hnu.edu.cn
  • Supported by:
    The authors were supported by NSFC (11771132) and Hunan Science and Technology Project (2018JJ1004).

摘要: In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p>1 and q>1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

关键词: q-torsional rigidity, Lp Minkowski problem, Lp Hadamard variational formula, Lp Brunn-Minkowski inequality

Abstract: In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p>1 and q>1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

Key words: q-torsional rigidity, Lp Minkowski problem, Lp Hadamard variational formula, Lp Brunn-Minkowski inequality

中图分类号: 

  • 35A02