21 citations · 34 across the 22 of their papers we have counts for
24 papers
Coarse geometry of metric measure spaces
Takayuki Okuda, Takashi Shioya
Using ideas from optimal transport theory, we introduce a notion of measured coarse equivalence for metric measure spaces and define a corresponding variant of the uniformly finite…
Hopf quotients of the infinite-dimensional Gaussian pyramid
Takashi Shioya, Shigeaki Yokota
We study the infinite-dimensional Gaussian pyramid and its quotients by the global sign flip and the -Hopf action. We resolve affirmatively a long-standing problem posed by T…
Two-dimensional metric spaces with curvature bounded above II
Koichi Nagano, Takashi Shioya, Takao Yamaguchi
As a continuation of \cite{NSY:local}, we mainly discuss the global structure of two-dimensional locally compact geodesically complete metric spaces with curvature bounded above. W…
Principal bundle structure of the space of metric measure spaces
Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya
We study the topological structure of the space of isomorphism classes of metric measure spaces equipped with the box or concentration topologies. We consider the sca…
Topological aspects of the space of metric measure spaces
Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence t…
A natural compactification of the Gromov-Hausdorff space
Hiroki Nakajima, Takashi Shioya
In this paper, we introduce a pseudometric on the family of isometry classes of (extended) metric spaces. Using it, we obtain a natural compactification of the Gromov-Hausdorff spa…