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.
Tsuji, Potential theory in modern function theory, M aruzen Co., Ltd., Tokyo
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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.