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math.MG2023
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…
math.MG2023
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…
math.MG2020
High-dimensional ellipsoids converge to Gaussian spaces
Daisuke Kazukawa, Takashi Shioya
We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered ex…