Accepted Paper

Inserted: 12 sep 2023
Last Updated: 13 sep 2024

Journal: ESAIM: COCV
Year: 2023
Doi: https://doi.org/10.1051/cocv/2024068

Abstract:

We characterize the maximizers of a functional involving the minimization of the Wasserstein distance between equal volume sets. This functional appears as a repulsive interaction term in some models describing biological membranes. We combine a symmetrization-by-reflection technique with the uniqueness of optimal transport plans to prove that balls are the only maximizers. Further, in one dimension, we provide a sharp quantitative version of this maximality result.