Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - N. Gigli

Construction of the parallel transport in the Wasserstein space

created by ambrosio on 15 Apr 2008


Accepted Paper

Inserted: 15 apr 2008

Journal: Methods and Applications of Analysis
Year: 2008


In this paper we study the problem of parallel transport in the

spaces of probability measures endowed with the quadratic optimal transport distence. We show that the

parallel transport exists along a class of curves whose velocity

field is sufficiently smooth, and that we call regular. Furthermore,

we show that the class of regular curves is dense in the class of

absolutely continuous curves and discuss the problem of parallel

transport along geodesics. Most results are extracted from the

PhD thesis of the second author.

Keywords: optimal transportation, Wasserstein distance, Parallel transport


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