Geodesic
First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 723-735

Voir la notice de l'article provenant de la source Cambridge University Press

We extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces $X$ with curvature bounded below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein space $\left( \mathcal{P}\left( X \right),\,{{W}_{2}} \right)$ satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obtained by proving a first variation formula for the Wasserstein distance.
DOI : 10.4153/CMB-2011-110-3
Mots-clés : 53C23, 28A35, 49Q20, 58A35, Alexandrov spaces, Wasserstein spaces, first variation formula, gradient flow 
Gigli, Nicola; Ohta, Shin-Ichi. First Variation Formula in Wasserstein Spaces over Compact Alexandrov Spaces. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 723-735. doi: 10.4153/CMB-2011-110-3
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