31 citations · 110 across the 36 of their papers we have counts for
5 papers · 1 filter
Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications
Alexandru Kristály, Shin-ichi Ohta
We prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli-Kohn-Nirenberg inequality with the same exponent , then it has exactly t…
Topology of complete Finsler manifolds with radial flag curvature bounded below
Kei Kondo, Shin-ichi Ohta, Minoru Tanaka
We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangol…
A Toponogov type triangle comparison theorem in Finsler geometry
Kei Kondo, Shin-ichi Ohta, Minoru Tanaka
The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation th…
Weighted Ricci curvature estimates for Hilbert and Funk geometries
Shin-ichi Ohta
We consider Hilbert and Funk geometries on a strongly convex domain in the Euclidean space. We show that, with respect to the Lebesgue measure on the domain, Hilbert (resp. Funk) m…
Splitting theorems for Finsler manifolds of nonnegative Ricci curvature
Shin-ichi Ohta
We investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger-Gromoll-Lichnerowicz splittin…