Work

Riesz Energy with a Radial External Field: When is the Equilibrium Support a Sphere?

Year: 2024

Type: article

Abstract: We consider Riesz energy problems with radial external fields. We study the question of whether or not the equilibrium measure is the uniform distribution on a sphere. We develop general necessary and general sufficient conditions on the external field that apply to powers of the Euclidean norm as well as certain Lennard – Jones type fields. Additionally, in the former case, we completely characterize the values of the power for which a certain dimension reduction phenomenon occurs: the support of the equilibrium measure becomes a sphere. We also briefly discuss the relationship between these problems and certain constrained optimization problems. Our approach involves the Frostman characterization, the Funk–Hecke formula, and the calculus of hypergeometric functions.

Source: Potential Analysis

DOI: 10.1007/s11118-024-10186-w

Authors: Djalil Chafaï, Ryan W. Matzke, Edward B. Saff, Minh Quan H. Vu, Robert S. Womersley

Institutions: Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département de mathématiques et applications, Vanderbilt University, UNSW Sydney

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: National Science Foundation, University of New South Wales