分野別セミナー

We generalize the theory of gradient flows of semi-convex functions established by Ambrosio-Gigli-Savaré for CAT(0)-spaces to CAT(1)-spaces. We show that the so called commutativity property and semi-convexity of the squared distance function is enough to establish the uniqueness, EVI and contractivity of the gradient flow similarly to the CAT(0) setting using the Moreau-Yoshida resolvent. The commutativity property is representing the Riemannian nature of the space.