3 citations · 6 across the 6 of their papers we have counts for
6 papers · 1 filter
An intrinsic characterization of five points in a space
Tetsu Toyoda
Gromov (2001) and Sturm (2003) proved that any four points in a space satisfy a certain family of inequalities. We call those inequalities the -inequal…
A non-geodesic analogue of Reshetnyak's majorization theorem
Tetsu Toyoda
For any real number and any integer , the condition introduced by Gromov (2001) is a necessary condition for a metric space to admit an isometric…
Uniform estimates of nonlinear spectral gaps
Takefumi Kondo, Tetsu Toyoda
By generalizing the path method, we show that nonlinear spectral gaps of a finite connected graph are uniformly bounded from below by a positive constant which is independent of th…
Fixed point property for a CAT(0) space which admits a proper cocompact group action
Tetsu Toyoda
We prove that if a geodesically complete space admits a proper cocompact isometric action of a group, then the Izeki-Nayatani invariant of is less than $1…
Random groups have fixed points on CAT(0) cube complexes
Koji Fujiwara, Tetsu Toyoda
We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.
CAT(0) spaces on which a certain type of singularity is bounded
Tetsu Toyoda
In this paper, we present a geometric condition for a family of CAT(0) spaces, which ensures that the Izeki-Nayatani invariants of spaces in the family are uniformly bounded from a…