Abstract
AbstractWe 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 ((X),W2) 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.
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