Calculus of Variations and Geometric Measure Theory
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N. Gigli - T. Rajala - K. T. Sturm

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

created by gigli on 21 May 2013


Submitted Paper

Inserted: 21 may 2013
Last Updated: 21 may 2013

Year: 2013


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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