Asian Journal of Mathematics

Volume 28 (2024)

Number 1

The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity for $p \gt 1$ and $\mathfrak{p} \geqslant n^\ast$

Pages: 47 – 78

DOI: https://dx.doi.org/10.4310/AJM.2024.v28.n1.a2

Authors

Xinbao Lu (School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications(Ministry of Education), Tongji University, Shanghai, China)

Ge Xiong (School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications(Ministry of Education), Tongji University, Shanghai, China)

Jiawei Xiong (School of Mathematics and Statistics, Ningbo University, Ningbo, China)

Abstract

The existence and uniqueness of solutions to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity for $p \gt 1$ and $\mathfrak{p} \geqslant n$ are proved. For this task, the estimation of $\mathfrak{p}$−capacitary measure controlled below by the surface area measure is achieved. This work is a sequel to the results $\href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ for $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$.

Keywords

$L_p$ Minkowski problem, capacity, capacitary measure

2010 Mathematics Subject Classification

31B15, 52A20

Full Text (PDF format)

Research of the authors was supported by NSFC No. 12271407.

Received 4 December 2022

Accepted 10 July 2023

Published 7 August 2024