Finiteness and realization theorems for Alexandrov spaces with bounded curvature

2019 ◽  
Vol 26 (2) ◽  
pp. 749-756
Author(s):  
Fernando Galaz-García ◽  
Wilderich Tuschmann
Keyword(s):  
Alexandrov Spaces ◽  
Bounded Curvature

scholarly journals Remarks on Manifolds with Two-Sided Curvature Bounds

2021 ◽  
Vol 9 (1) ◽  
pp. 53-64
Author(s):  
Vitali Kapovitch ◽  
Alexander Lytchak
Keyword(s):  
Distance Functions ◽  
Cut Locus ◽  
Bounded Curvature ◽  
Curvature Bounds ◽  
Positive Reach

Abstract We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

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 Elastic multi-particle systems for bounded-curvature path planning

2008 ◽  
Author(s):  
Ali Ahmadzadeh ◽  
Ali Jadbabaie ◽  
George J. Pappas ◽  
Vijay Kumar
Keyword(s):  
Path Planning ◽  
Particle Systems ◽  
Bounded Curvature

Minimal surfaces in R 3 with one end¶and bounded curvature

1998 ◽  
Vol 96 (1) ◽  
pp. 3-7 ◽  
Author(s):  
Lucio Rodríguez ◽  
Harold Rosenberg
Keyword(s):  
Minimal Surfaces ◽  
Bounded Curvature
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