5 papers
Toward Pólya and Szegő's conjecture for logarithmic vs Newtonian capacity
Carrie Clark, Richard S. Laugesen
Pólya and Szegő conjectured in 1945 that the disk achieves the largest electrostatic capacity among all planar sets with given logarithmic capacity. This question generalizes natur…
Riesz energy deformation through insulated strips
Carrie Clark, Richard S. Laugesen
For compact sets in Euclidean space, Riesz energies whose exponents differ by are shown to arise as the endpoint cases of a one-parameter family of infinite-strip energies as t…
Maximizing Riesz capacity ratios: conjectures and theorems
Carrie Clark, Richard S. Laugesen
A shape optimization program is developed for the ratio of Riesz capacities , where ranges over compact sets in . In different re…
Riesz capacity: monotonicity, continuity, diameter and volume
Carrie Clark, Richard S. Laugesen
Properties of Riesz capacity are developed with respect to the kernel exponent , namely that capacity is monotonic as a function of , that its endpoint limits…
Balls minimize moments of logarithmic and Newtonian equilibrium measures
Carrie Clark, Richard S. Laugesen
The -th moment () of electrostatic equilibrium measure is shown to be minimal for a centered ball among -dimensional sets of given capacity, while among -dimensional…