2 citations · 2 across the 5 of their papers we have counts for
5 papers
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…