7 citations · 18 across the 16 of their papers we have counts for
16 papers
The disjoint disks property for Busemann -spaces
Tadashi Fujioka, Shijie Gu
We prove that every finite-dimensional Busemann \(G\)-space of dimension at least five has the disjoint disks property (DDP). For a sufficiently small metric sphere \(L=S(c,r)\), w…
Busemann G-spaces with convex balls
Tadashi Fujioka, Shijie Gu
We prove that any Busemann G-space such that every sufficiently small metric ball is convex is a topological manifold. The key ingredient in the proof is Ivanov's Helly theorem. Th…
Finsler structure of Busemann G-spaces
Tadashi Fujioka, Shijie Gu
We provide two sufficient conditions for a Busemann G-space to admit a differentiable DC atlas with a continuous Finsler metric, from the viewpoint of comparison geometry. These re…
Busemann and MCP
Tadashi Fujioka, Kenshiro Tashiro
We study the structure of Busemann spaces with measures satisfying the measure contraction property (MCP). The main results are rigidity theorems and structure theorems under the a…
Topological regularity of Busemann spaces of nonpositive curvature
Tadashi Fujioka, Shijie Gu
We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We g…
Alexandrov spaces are CS sets
Tadashi Fujioka
We prove that the extremal stratification of an Alexandrov space introduced by Perelman-Petrunin is a CS stratification in the sense of Siebenmann. We also show that every space of…
A lower bound for the curvature integral under an upper curvature bound
Tadashi Fujioka
We prove that the integral of scalar curvature over a Riemannian manifold is uniformly bounded below in terms of its dimension, upper bounds on sectional curvature and volume, and…
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.…
Extremal subsets in geodesically complete spaces with curvature bounded above
Tadashi Fujioka
We introduce the notion of an extremal subset in a geodesically complete space with curvature bounded above, i.e., a GCBA space. This is an analogue of an extremal subset in an Ale…
Euler characteristics of collapsing Alexandrov spaces
Tadashi Fujioka
We prove that the Euler characteristic of a collapsing Alexandrov space (in particular, a Riemannian manifold) is equal to the sum of the products of the Euler characteristics with…
Collapsing to Alexandrov spaces with isolated mild singularities
Tadashi Fujioka
Let be a sequence of Riemannian manifolds with sectional curvature bound below collapsing to a compact Alexandrov space of dimension . Suppose that all but finitely ma…
Noncritical maps on geodesically complete spaces with curvature bounded above
Tadashi Fujioka
We define and study the regularity of distance maps on geodesically complete spaces with curvature bounded above. We prove that such a regular map is locally a Hurewicz fibration.…
Application of good coverings to collapsing Alexandrov spaces
Tadashi Fujioka
Let be an Alexandrov space collapsing to an Alexandrov space of lower dimension. Suppose has no proper extremal subsets and let denote a regular fiber. We slightly…
A fibration theorem for collapsing sequences of Alexandrov spaces
Tadashi Fujioka
Suppose a sequence of Alexandrov spaces collapses to a space with only weak singularities. Yamaguchi constructed a map called an almost Lipschitz submersio…
Regular points of extremal subsets in Alexandrov spaces
Tadashi Fujioka
We define regular points of an extremal subset in an Alexandrov space and study their basic properties. We show that a neighborhood of a regular point in an extremal subset is almo…
Uniform boundedness on extremal subsets in Alexandrov spaces
Tadashi Fujioka
In this paper, we study extremal subsets in Alexandrov spaces with dimension , curvature , and diameter . We show that the following three quantities are uniformly…