A Minkowski Theory for the Exterior Capacitary Volumes and A Resolution of the Pólya-Szegö Conjecture

2026/07/31 by Qiushuang Liu, Jie Xiao, Ning Zhang +2
Mathematics · #math.MG #math.FA #msc:52A40 #msc:31B15 #msc:35J92 #msc:52A20 #msc:35P30

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The main reference we use is wrong

arxiv created 2026/07/31 · arxiv updated 2026/08/04

Abstract

This paper establishes a unified Minkowski theory for exterior p-capacitary volumes and resolves the classical Pólya-Szegö conjecture on the electrostatic capacity of convex bodies.

Citations

• Charge densities for conducting ellipsoids
• Radial symmetry for p-harmonic functions in exterior and punctured domains
• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems
• p-capacity vs surface-area
• A Maximum Problem of S.-T. Yau for Variational p-Capacity
• p Harmonic Measure in Simply Connected Domains