6 citations · 23 across the 16 of their papers we have counts for
16 papers
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…
Collapsing three-dimensional Alexandrov spaces with boundary
Ayato Mitsuishi, Takao Yamaguchi
As a continuation of [MY], we determine the topologies of collapsing three-dimensional compact Alexandrov spaces with nonempty boundary.
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…
Lipschitz homotopy convergence of Alexandrov spaces II
Tadashi Fujioka, Ayato Mitsuishi, Takao Yamaguchi
We establish a quantitative version of the Lipschitz homotopy convergence introduced by Mitsuishi and Yamaguchi for a moduli space of compact Alexandrov spaces without collapsing.…
Principal eigenvalue problem for infinity Laplacian in metric spaces
Qing Liu, Ayato Mitsuishi
This paper is concerned with the Dirichlet eigenvalue problem associated to the -Laplacian in metric spaces. We establish a direct PDE approach to find the principal eigenv…
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…
Certain min-max values related to the -energy and packing radii of Riemannian manifolds and metric measure spaces
Ayato Mitsuishi
Grosjean proved that the -th power of the first eigenvalue of the -Laplacian on a closed Riemannian manifold converges to the twice of the inverse of the diameter of the…
Obtuse constants of Alexandrov spaces
Ayato Mitsuishi, Takao Yamaguchi
We introduce a new geometric invariant called the obtuse constant of spaces with curvature bounded below. We first find relations between this invariant and the normalized volume.…
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…
The coincidence of the current homology and the measure homology via a new topology on spaces of Lipschitz maps
Ayato Mitsuishi
We consider the category of all locally Lipschitz contractible metric spaces and all locally Lipschitz maps, which is a wide class of metric spaces, including all finite dimensiona…
The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves
Ayato Mitsuishi
We consider the notion of metric spaces being locally Lipschitz contractible introduced by Yamaguchi, and a category of metric spaces satisfying this condition. Many objects in met…
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.