Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature

Jordan Serres

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arXiv · 2508.13688

Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature

Jordan Serres

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Abstract

We prove that every nearly spherical, positively curved surface is the contractive, volume-preserving image of a round sphere. The proof combines three main tools: the Ricci flow on surfaces, the Kim-Milman construction, and a multiscale Bakry-\'Emery criterion.

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Jordan Serres. 2025-08-19. Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature. https://arxiv.org/abs/2508.13688

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