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math.MG2014
Gradient flows and a Trotter--Kato formula of semi-convex functions on CAT(1)-spaces
Shin-ichi Ohta, Miklós Pálfia
We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savaré, to CAT(1)-spaces. The key tool is the so-calle…
math.MG2014
Discrete-time gradient flows and law of large numbers in Alexandrov spaces
Shin-ichi Ohta, Miklós Pálfia
We develop the theory of discrete-time gradient flows for convex functions on Alexandrov spaces with arbitrary upper or lower curvature bounds. We employ different resolvent maps i…