4 papers · 1 filter
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…
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…
Convergence of metric transformed spaces
Daisuke Kazukawa
We consider the metric transformation of metric measure spaces/pyramids. We clarify the conditions to obtain the convergence of the sequence of transformed spaces from that of the…
Convergence of energy functionals and stability of lower bounds of Ricci curvature via metric measure foliation
Daisuke Kazukawa
The notion of the metric measure foliation is introduced by Galaz-García, Kell, Mondino, and Sosa. They studied the relation between a metric measure space with a metric measure fo…