31 citations · 110 across the 36 of their papers we have counts for
7 papers · 1 filter
A generalization of Grünbaum's inequality in RCD-spaces
Victor-Emmanuel Brunel, Shin-ichi Ohta, Jordan Serres
We generalize Grünbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to -spaces with …
Barycenters and a law of large numbers in Gromov hyperbolic spaces
Shin-ichi Ohta
We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces. We establish a contraction…
Self-contracted curves in spaces with weak lower curvature bound
Nina Lebedeva, Shin-ichi Ohta, Vladimir Zolotov
We show that bounded self-contracted curves are rectifiable in metric spaces with weak lower curvature bound in a sense we introduce in this article. This class of spaces is wide a…
Self-contracted curves in CAT(0)-spaces and their rectifiability
Shin-ichi Ohta
We investigate self-contracted curves, arising as (discrete or continuous time) gradient curves of quasi-convex functions, and their rectifiability (finiteness of the lengths) in E…
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…
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…
Markov type of Alexandrov spaces of nonnegative curvature
Shin-ichi Ohta
We prove that Alexandrov spaces of nonnegative curvature have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz continuous map from a subset of into a 2-uni…