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math.AP2025
A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds
Yuxin Ge, Jordan Serres
We show that every nearly spherical manifold can be realized as the volume-preserving image of a round sphere, via the Brenier-McCann optimal transport map. This theorem extends Ca…
math.ST2025★ 1 cited
Finite sample bounds for barycenter estimation in geodesic spaces
Victor-Emmanuel Brunel, Jordan Serres
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support con…