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Award ID contains: 2306962

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  1. ; ; (, The American Mathematical Monthly)
    Free, publicly-accessible full text available June 9, 2026
  2. ; (, Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications)
    We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exist curves in the perturbation-volume parameter space that separate stability/instability and global minimality/nonminimality regions of the ball, and provide a precise description of these curves for certain interaction kernels. In particular, we show that in small perturbation regimes there are (at least) two disconnected regions for the mass parameter in which the ball is stable, separated by an instability region. 
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    Free, publicly-accessible full text available June 6, 2026
  3. ; ; (, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)
    Recently it has been shown that the unique local perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens, hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem. 
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    Free, publicly-accessible full text available January 27, 2026
  4. ; ; (, Pure and Applied Analysis)
    We consider a non-local interaction energy over bounded densities of fixed mass m. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when m is sufficiently small (or even for every m, in particular cases). We show that these assumptions are satisfied by particular interaction kernels in power-law form, and give a certain characterization of minimizing sets. Finally, following a recent result of Davies, Lim and McCann, we give sufficient conditions on the interaction kernel so that the minimizer of the energy over probability measures is given by Dirac masses concentrated on the vertices of a regular (N+1)-gon of side length 1 in R^N. 
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    Free, publicly-accessible full text available November 17, 2025
  5. ; ; (, ESAIM: Control, Optimisation and Calculus of Variations)
    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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