In this paper we study the problem of parallel transport in the Wasserstein spaces P_2(R^d). 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
Construction of the parallel transport in the Wasserstein space / Gigli, Nicola; Ambrosio, Luigi. - In: METHODS AND APPLICATIONS OF ANALYSIS. - ISSN 1073-2772. - 15:1(2008), pp. 1-30.
Construction of the parallel transport in the Wasserstein space
Gigli, Nicola;
2008-01-01
Abstract
In this paper we study the problem of parallel transport in the Wasserstein spaces P_2(R^d). 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| File | Dimensione | Formato | |
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