Zobrazeno 1 - 10
of 178
pro vyhledávání: '"Ohta Shin-ichi"'
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 10, Iss 1, Pp 1-30 (2022)
We establish the Bonnet–Myers theorem, Laplacian comparison theorem, and Bishop–Gromov volume comparison theorem for weighted Finsler manifolds as well as weighted Finsler spacetimes, of weighted Ricci curvature bounded below by using the weight
Externí odkaz:
https://doaj.org/article/60a609569a0b4ba9a0047f193e677581
We generalize Gr\"unbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to $\mathrm{RCD}(0,N)$-spaces with $N \in (1,\infty)$ as well as weighted Riemannian manifolds of $\mathrm{Ric}_N \ge 0$
Externí odkaz:
http://arxiv.org/abs/2408.15030
Autor:
Ohta, Shin-ichi, Suzuki, Kohei
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 establishing a Varadhan-type formula for non-linear semigroups. We do not assume
Externí odkaz:
http://arxiv.org/abs/2403.04102
Autor:
Braun, Mathias, Ohta, Shin-ichi
Publikováno v:
Trans. Amer. Math. Soc. 377 (2024), 3529-3576
We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature $\smash{\mathrm{Ric}_N}$ is bounded from below by a real number $K$ in every timelike direction satisfies the timelike curvature-dimensio
Externí odkaz:
http://arxiv.org/abs/2305.04389
Autor:
Ohta, Shin-ichi
Publikováno v:
Rev. Mat. Iberoam. 40 (2024), 1185-1206
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 property (the Wasserstein distance between probability measures provi
Externí odkaz:
http://arxiv.org/abs/2211.00193
Autor:
Ohta, Shin-ichi, Zhao, Wei
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and upper gradi
Externí odkaz:
http://arxiv.org/abs/2206.07591
Autor:
Ohta Shin-ichi
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 2, Iss 1 (2014)
We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-W
Externí odkaz:
https://doaj.org/article/03584fdc10964c6fb51035739f821ca4
Autor:
Ohta, Shin-ichi
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 algorithm from an arbitrary initial point can find a point close to a
Externí odkaz:
http://arxiv.org/abs/2205.03156
Autor:
Mai, Cong Hung, Ohta, Shin-ichi
Publikováno v:
Bull. Lond. Math. Soc. 55 (2023), 224-233
Concerning quantitative isoperimetry for a weighted Riemannian manifold satisfying $\mathrm{Ric}_{\infty} \ge 1$, we give an $L^1$-estimate exhibiting that the push-forward of the reference measure by the guiding function (arising from the needle dec
Externí odkaz:
http://arxiv.org/abs/2203.03766