Carrie Clark

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math.CA2026

Riesz energy deformation through insulated strips

Carrie Clark, Richard S. Laugesen

For compact sets in Euclidean space, Riesz energies whose exponents differ by $1$ are shown to arise as the endpoint cases of a one-parameter family of infinite-strip energies as t…

math.CA2024

Maximizing Riesz capacity ratios: conjectures and theorems

Carrie Clark, Richard S. Laugesen

A shape optimization program is developed for the ratio of Riesz capacities $Cap_{q} (K) / Cap_{p} (K)$ , where $K$ ranges over compact sets in $R^{n}$ . In different re…

math.CA2024

Riesz capacity: monotonicity, continuity, diameter and volume

Carrie Clark, Richard S. Laugesen

Properties of Riesz capacity are developed with respect to the kernel exponent $p \in (- \infty, n)$ , namely that capacity is monotonic as a function of $p$ , that its endpoint limits…

math.CA2024

Balls minimize moments of logarithmic and Newtonian equilibrium measures

Carrie Clark, Richard S. Laugesen

The $q$ -th moment ( $q > 0$ ) of electrostatic equilibrium measure is shown to be minimal for a centered ball among $3$ -dimensional sets of given capacity, while among $2$ -dimensional…