First variation formula in Wasserstein spaces over compact Alexandrov spaces
نویسندگان
چکیده
We extend results proven by the second author ([Oh]) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spacesX with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(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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