9 citations · 16 across the 11 of their papers we have counts for
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Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes
Mathias Braun, Shin-ichi Ohta
We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature is bounded from below by a real number …
Gradient flows in asymmetric metric spaces and applications
Shin-ichi Ohta, Wei Zhao
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 discr…
Quantitative estimates for the Bakry-Ledoux isoperimetric inequality. II
Cong Hung Mai, Shin-ichi Ohta
Concerning quantitative isoperimetry for a weighted Riemannian manifold satisfying , we give an -estimate exhibiting that the push-forward of the…
Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem
Yufeng Lu, Ettore Minguzzi, Shin-ichi Ohta
We show an analogue of the Lorentzian splitting theorem for weighted Lorentz-Finsler manifolds: If a weighted Berwald spacetime of nonnegative weighted Ricci curvature satisfies ce…
Comparison theorems on weighted Finsler manifolds and spacetimes with -range
Yufeng Lu, Ettore Minguzzi, Shin-ichi Ohta
We establish the Bonnet-Myers theorem, Laplacian comparison theorem, and Bishop-Gromov volume comparison theorem for weighted Finsler manifolds as well as weighted Finsler spacetim…
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…