scholarly journals A Fibration Theorem for Collapsing Sequences of Alexandrov Spaces

2021 ◽  
Author(s):  
Tadashi Fujioka
Keyword(s):  
Alexandrov Spaces

scholarly journals The Riemannian structure of Alexandrov spaces

1994 ◽  
Vol 39 (3) ◽  
pp. 629-658 ◽  
Author(s):  
Yukio Otsu ◽  
Takashi Shioya
Keyword(s):  
Riemannian Structure ◽  
Alexandrov Spaces

scholarly journals Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 787-798 ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Diameter Growth ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Finite Generation ◽  
Alexandrov Spaces ◽  
Geodesic Spaces ◽  
Special Case ◽  
Linear Diameter

AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

scholarly journals A topological splitting theorem for weighted Alexandrov spaces

2011 ◽  
Vol 63 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Kazuhiro Kuwae ◽  
Takashi Shioya
Keyword(s):  
Splitting Theorem ◽  
Alexandrov Spaces

scholarly journals The Sormani–Wenger intrinsic flat convergence of Alexandrov spaces

2018 ◽  
Vol 12 (03) ◽  
pp. 819-839 ◽  
Author(s):  
Nan Li ◽  
Raquel Perales
Keyword(s):  
Regular Point ◽  
Dimensional Sphere ◽  
Volume Estimate ◽  
Alexandrov Spaces ◽  
Filling Volume ◽  
Integral Current ◽  
Structure Formula ◽  
Intrinsic Flat ◽  
Dimensional Integral ◽  
Uniformly Bounded

We study sequences of integral current spaces [Formula: see text] such that the integral current structure [Formula: see text] has weight [Formula: see text] and no boundary and, all [Formula: see text] are closed Alexandrov spaces with curvature uniformly bounded from below and diameter uniformly bounded from above. We prove that for such sequences either their limits collapse or the Gromov–Hausdorff and Sormani–Wenger Intrinsic Flat limits agree. The latter is done showing that the lower [Formula: see text]-dimensional density of the mass measure at any regular point of the Gromov–Hausdorff limit space is positive by passing to a filling volume estimate. In an appendix, we show that the filling volume of the standard [Formula: see text]-dimensional integral current space coming from an [Formula: see text]-dimensional sphere of radius [Formula: see text] in Euclidean space equals [Formula: see text] times the filling volume of the [Formula: see text]-dimensional integral current space coming from the [Formula: see text]-dimensional sphere of radius [Formula: see text].

scholarly journals Locally Lipschitz contractibility of Alexandrov spaces and its applications

2014 ◽  
Vol 270 (2) ◽  
pp. 393-421 ◽  
Author(s):  
Ayato Mitsuishi ◽  
Takao Yamaguchi
Keyword(s):  
Alexandrov Spaces ◽  
Locally Lipschitz
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