A symmetry problem

2004/11/08 by A. G. Ramm, А. Г. Рамм, Ramm, A. G.
Mathematics · #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematics and Applications #math.AP #msc:35R30

paper · pdf · doi:10.48550/arxiv.math/0411175

arxiv created 2004/11/08 · openalex publication_date 2004/11/08 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The following result is proved: \bf Theorem. Let D⊂ \R³ be a bounded domain homeomorphic to a ball, |D| be its volume, |S| be the surface area of its smooth boundary S, D⊂ B_R:=\x:|x|≤ R\, and H_R is the set of all harmonic in B_R functions. If \frac 1 |D|∫_Dhdx=\frac 1 |S|∫_Shds ∀ h∈ H_R, then D is a ball.

Related

• Symmetry problems in harmonic analysis
• Symmetry from sectional integrals for convex domains
• Solution to the Pompeiu problem and the related symmetry problem
• A characterization of the ball
• Symmetry of minimizers with a level surface parallel to the boundary