2 citations · 2 across the 9 of their papers we have counts for
10 papers
Topological dimension of the Gromov-Hausdorff and Gromov-Prokhorov spaces
Hiroki Nakajima, Takamitsu Yamauchi, Nicolò Zava
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure…
Extension of Gromov's Lipschitz order to with additive errors
Hiroki Nakajima
Gromov's Lipschitz order is an order relation on the set of metric measure spaces. One of the compactifications of the space of isomorphism classes of metric measure spaces equippe…
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…
Box distance and observable distance via optimal transport
Hiroki Nakajima
On the set of all metric measure spaces, we have two important metrics, the box metric and the observable metric, both introduced by M. Gromov. We obtain the representation of thes…
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…
Convergence of group actions in metric measure geometry
Hiroki Nakajima, Takashi Shioya
We generalize the box and observable distances to those between metric measure spaces with group actions, and prove some fundamental properties. As an application, we obtain an exa…
Isoperimetric inequality on a metric measure space and Lipschitz order with an additive error
Hiroki Nakajima
M. Gromov introduced the Lipschitz order relation on the set of metric measure spaces and developed a rich theory. In particular, he claimed that an isoperimetric inequality on a n…
Isoperimetric rigidity and distributions of 1-Lipschitz functions
Hiroki Nakajima, Takashi Shioya
We prove that if a geodesic metric measure space satisfies a comparison condition for isoperimetric profile and if the observable variance is maximal, then the space is foliated by…
The maximum of the 1-measurement of a metric measure space
Hiroki Nakajima
For a metric measure space, we treat the set of distributions of 1-Lipschitz functions, which is called the 1-measurement. On the 1-measurement, we have a partial order relation by…