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arXiv · 2309.05522

Maximizers of nonlocal interactions of Wasserstein type

Almut Burchard·Davide Carazzato·Ihsan Topaloglu
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Abstract

We characterize the maximizers of a functional that involves the minimization of the Wasserstein distance between sets of equal volume. We prove that balls are the only maximizers by combining a symmetrization-by-reflection technique with the uniqueness of optimal transport plans. Further, in one dimension, we provide a sharp quantitative refinement of this maximality result.

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Almut Burchard, Davide Carazzato, Ihsan Topaloglu. 2023-09-11. Maximizers of nonlocal interactions of Wasserstein type. https://arxiv.org/abs/2309.05522

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