7 papers
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…
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…
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…
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…
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.…