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arXiv · 1305.4849

Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below

Nicola Gigli·Tapio Rajala·Karl-Theodor Sturm
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Abstract

We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.

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Nicola Gigli, Tapio Rajala, Karl-Theodor Sturm. 2013-05-21. Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below. https://arxiv.org/abs/1305.4849

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