Institute of Mathematics for Industry

Seminar



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Gradient flows in K-convex and CAT(1)-spaces


Hold Date 2015-01-23 16:00~2015-01-23 17:30

Place Seminar Room 2, Faculty of Mathematics building, Ito Campus

Object person researchers and graduate students 

Speaker Miklos PALFIA (Kyoto University)

Abstract:
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.