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 (P(X),W_2) 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. © Canadian Mathematical Society 2011.
First variation formula in Wasserstein spaces over compact Alexandrov spaces
Gigli, Nicola;
2012-01-01
Abstract
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 (P(X),W_2) 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. © Canadian Mathematical Society 2011.File in questo prodotto:
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