11 citations · 43 across the 12 of their papers we have counts for
12 papers
Two-dimensional metric spaces with curvature bounded above I
Koichi Nagano, Takashi Shioya, Takao Yamaguchi
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz…
Hausdorff dimension of asymptotic self-similar sets
Daruhan Wu, Takao Yamaguchi
In this paper, we introduce the notion of asymptotic self-similar sets on general doubling metric spaces by extending the notion of self-similar sets, and determine their Hausdorff…
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…
Inradius collapsed manifolds
Takao Yamaguchi, Zhilang Zhang
In this paper, we study collapsed manifolds with boundary, where we assume a lower sectional curvature bound, two sides bounds on the second fundamental forms of boundaries and upp…
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…