From the 1 of 6 linked papers with an AI index.
6 papers
A Brenier-Strassen Theorem on CAT(kappa) Spaces
Nathael Gozlan, Hugo Malamut, Shin-Ichi Ohta
The paper generalizes the Brenier‑Strassen theorem to spaces with curvature bounded above, proving existence and uniqueness of a Wasserstein‑2 projection onto measures dominated in…
Brownian motion in Minkowski normed spaces
Shin-ichi Ohta, Marco Rehmeier, Kohei Suzuki
A Minkowski normed space is the Euclidean space equipped with a (possibly asymmetric) uniformly convex and smooth norm, forming a particular class of Finsler manifolds. We construc…
Discrete-time gradient flows for unbounded convex functions on Gromov hyperbolic spaces
Shin-ichi Ohta
In proper, geodesic Gromov hyperbolic spaces, we investigate discrete-time gradient flows via the proximal point algorithm for unbounded Lipschitz convex functions. Assuming that t…
How does the contraction property fail for convex functions on normed spaces?
Shin-ichi Ohta
On Euclidean and Hilbert spaces, Riemannian manifolds, and CAT-spaces, gradient flows of convex functions are known to satisfy the contraction property, which plays a fundamen…
Integral Varadhan formula for non-linear heat flow
Shin-ichi Ohta, Kohei Suzuki
We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishi…
Discrete-time gradient flows in Gromov hyperbolic spaces
Shin-ichi Ohta
We investigate fundamental properties of the proximal point algorithm for Lipschitz convex functions on (proper, geodesic) Gromov hyperbolic spaces. We show that the proximal point…