6 citations · 23 across the 16 of their papers we have counts for
9 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…
Distance functions on convex bodies and symplectic toric manifolds
Hajime Fujita, Yu Kitabeppu, Ayato Mitsuishi
In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplec…
Lipschitz homotopy convergence of Alexandrov spaces
Ayato Mitsuishi, Takao Yamaguchi
We introduce the notion of good coverings of metric spaces, and prove that if a metric space admits a good covering, then it has the same locally Lipschitz homotopy type as the ner…
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…
Self and partial gluing theorems for Alexandrov spaces with a lower curvature bound
Ayato Mitsuishi
This paper is devoted to prove that if an Alexandrov space of curvature not less than with a codimension one extremal subset which admits an isometric involution with respect t…
Good coverings of Alexandrov spaces
Ayato Mitsuishi, Takao Yamaguchi
In the present paper, we define a notion of good coverings of Alexandrov spaces with curvature bounded below, and prove that every Alexandrov space admits such a good covering and…
Locally Lipschitz contractibility of Alexandrov spaces and its applications
Ayato Mitsuishi, Takao Yamaguchi
We prove that any finite dimensional Alexandrov space with a lower curvature bound is locally Lipschitz contractible. As applications, we obtain a sufficient condition for solving…
Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound
Ayato Mitsuishi, Takao Yamaguchi
In the present paper, we determine the topologies of three-dimensional closed Alexandrov spaces which converge to lower dimensional spaces in the Gromov-Hausdorff topology.