Proves Wasserstein inequality bounding transport cost by Green's function sum, implying optimal W2 rate for minimal Green energy point sets on manifolds and Coulomb energy on spheres.
On the separation distance of minimal Green energy points on compact Riemannian manifolds
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abstract
In this article we study point configurations minimizing the discrete energy on a compact Riemannian manifold, where the energy kernel is taken to be the Green's function for the Laplacian. We show that every point in a minimizing configuration lies inside an open set called harmonic ball where no other point can enter, and that the minimum distance between any two distinct points has the optimal asymptotic order. We compute explicit bounds for the minimum distance in the case of Compact Rank One Symmetric Spaces.
years
2019 2verdicts
UNVERDICTED 2representative citing papers
For sufficiently large equal charges, the boundary of the equilibrium droplet on the sphere is the stereographic projection of an ellipse, and a mother body is obtained from a weakly admissible equilibrium problem on the real line.
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A Wasserstein Inequality and Minimal Green Energy on Compact Manifolds
Proves Wasserstein inequality bounding transport cost by Green's function sum, implying optimal W2 rate for minimal Green energy point sets on manifolds and Coulomb energy on spheres.
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An equilibrium problem on the sphere with two equal charges
For sufficiently large equal charges, the boundary of the equilibrium droplet on the sphere is the stereographic projection of an ellipse, and a mother body is obtained from a weakly admissible equilibrium problem on the real line.