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November 2020 The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity
Zou Du, Xiong Ge
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J. Differential Geom. 116(3): 555-596 (November 2020). DOI: 10.4310/jdg/1606964418

Abstract

Existence and uniqueness of the solution to the $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity are proved when $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$. These results are nonlinear extensions of the very recent solution to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity when $p = 1$ and $1 \lt \mathfrak{p} \lt n$ by Colesanti et al. and Akman et al., and the classical solution to the Minkowski problem for electrostatic capacity when $p = 1$ and $\mathfrak{p} = 2$ by Jerison.

Funding Statement

Research of the authors was supported by NSFC No. 11871373 and NSFC No. 11601399.

Citation

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Zou Du. Xiong Ge. "The $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity." J. Differential Geom. 116 (3) 555 - 596, November 2020. https://doi.org/10.4310/jdg/1606964418

Information

Received: 2 March 2017; Published: November 2020
First available in Project Euclid: 3 December 2020

zbMATH: 07282210
MathSciNet: MR4182897
Digital Object Identifier: 10.4310/jdg/1606964418

Subjects:
Primary: 31B15 , 52A20

Keywords: $\mathfrak{p}$-capacity , Brunn–Minkowski theory , convex body , Minkowski problem

Rights: Copyright © 2020 Lehigh University

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Vol.116 • No. 3 • November 2020
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