ScienceAsia - Journal of The Science Society of Thailand

ABSTRACT: A characterization for a Riesz s-potential function of a multiset ω_N of N points in ℝ² is given when s=2−2N and the potential function is constant on a circle in ℝ². The characterization allows us to partially prove a conjecture of Nikolov and Rafailov that if the potential function is constant on a circle Γ then the points in ω_N should be equally spaced on a circle concentric to Γ. As an application of constant Riesz s-potential functions, we also find all maximal and minimal polarization constants and configurations of two concentric circles in ℝ² for certain values of s.

Constant Riesz potentials on a circle in a plane with an application to polarization optimality problems

Nattapong Bosuwan^a,b, Pornrat Ruengrot^c,*

Constant Riesz potentials on a circle in a plane with an application to polarization optimality problems

Nattapong Bosuwana,b, Pornrat Ruengrotc,*

Nattapong Bosuwan^a,b, Pornrat Ruengrot^c,*