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Creators/Authors contains: "Matzke, Ryan_W"

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  1. ; (, Archive for Rational Mechanics and Analysis)
    Abstract We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that in an optimal part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions. 
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  2. ; ; ; ; (, Potential Analysis)
    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. 
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