21 citations · 34 across the 22 of their papers we have counts for
7 papers · 1 filter
Graph manifolds as ends of negatively curved Riemannian manifolds
Koji Fujiwara, Takashi Shioya
Let be a graph manifold such that each piece of its JSJ decomposition has the geometry. Assume that the pieces are glued by isometries. Then, there exi…
Estimate of isodiametric constant for closed surfaces
Takashi Shioya
We give an explicit estimate of the area of a closed surface by the diameter and a lower bound of curvature. This is better than Calabi-Cao's estimate for a nonnegatively curved tw…
A topological splitting theorem for weighted Alexandrov spaces
Kazuhiro Kuwae, Takashi Shioya
Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-G…
Laplacian comparison for Alexandrov spaces
Kazuhiro Kuwae, Takashi Shioya
We consider an infinitesimal version of the Bishop-Gromov relative volume comparison condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces. We prov…
Variational convergence over metric spaces
Kazuhiro Kuwae, Takashi Shioya
We introduce a natural definition of -convergence of maps, , in the case where the domain is a convergent sequence of measured metric space with respect to the measur…
Fixed point sets of parabolic isometries of CAT(0)-spaces
Koji Fujiwara, Koichi Nagano, Takashi Shioya
We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most pi/2, and study its c…