31 citations · 110 across the 36 of their papers we have counts for
4 papers · 1 filter
Quantitative estimates for the Bakry-Ledoux isoperimetric inequality
Cong Hung Mai, Shin-ichi Ohta
We establish a quantitative isoperimetric inequality for weighted Riemannian manifolds with . Precisely, we give an upper bound of the volume of the sy…
Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems
Yufeng Lu, Ettore Minguzzi, Shin-ichi Ohta
We develop the theory of weighted Ricci curvature in a weighted Lorentz-Finsler framework and extend the classical singularity theorems of general relativity. In order to reach thi…
Equality in the logarithmic Sobolev inequality
Shin-ichi Ohta, Asuka Takatsu
We investigate the rigidity problem for the logarithmic Sobolev inequality on weighted Riemannian manifolds satisfying . Assuming equality holds, we…
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…