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math.MG2024
Convergence of cones of metric measure spaces and its application to Cauchy distribution
Syota Esaki, Daisuke Kazukawa, Ayato Mitsuishi
We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an applicati…
math.MG2023
Invariants for Gromov's pyramids and their applications
Syota Esaki, Daisuke Kazukawa, Ayato Mitsuishi
Pyramids introduced by Gromov are generalized objects of metric spaces with Borel probability measures. We study non-trivial pyramids, where non-trivial means that they are not rep…
math.MG2016★ 3 cited
Orientability and fundamental classes of Alexandrov spaces with applications
Ayato Mitsuishi
In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geo…