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arXiv · 2605.25086

Isoperimetric minimizing movements and AC curves in spaces of measures

Pietro Aldrigo
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Abstract

We define a complete metric structure on the family $\text{PL}_q^p(\mathbb{R}^n)$ of probability measures with densities in $L^p(\mathbb{R}^n)$ and finite $q$-moments. We establish the existence of generalized minimizing movements for the isoperimetric ratio and characterize absolutely continuous curves in this space through weak solutions of the continuity equation with velocity fields satisfying a first-order integral condition. We also characterize absolutely continuous curves in the $\infty$-Wasserstein space and prove a Benamou--Brenier formula for $W_\infty$.

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Pietro Aldrigo. 2026-05-24. Isoperimetric minimizing movements and AC curves in spaces of measures. https://arxiv.org/abs/2605.25086

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