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We give an if-and-only-if condition on a five-point metric spaces that admit embeddings into nonnegatively curved Riemannian manifolds.
‘‘Alexandrov geometry: foundations’’, 2022
S. Alexander, V. Kapovitch and A. Petrunin · 1903
Earlier work this paper cites.
‘‘Begründung eiiner Koordinatenlosen Differentialgeometrie der Flächen’’
A. Wald · 1935
Earlier work this paper cites.
‘‘Alexandrov paces with curvature bounded from below II.’’, Preprint LOMI, 1991
G. Perelman · 1991
Earlier work this paper cites.
‘‘Kirszbraun’s theorem and metric spaces of bounded curvature’’
U. Lang and V. Schroeder · 1997
Earlier work this paper cites.
‘‘Metric spaces of lower bounded curvature’’
K.-T. Sturm · 1999
Earlier work this paper cites.
‘‘Metric structures for Riemannian and non-Riemannian spaces’’, Modern Birkhäuser Classics, 2007
M. Gromov · 2007
Cited alongside, same era.
‘‘Alexandrov meets Kirszbraun’’
S. Alexander, V. Kapovitch and A. Petrunin · 2011
Cited alongside, same era.
‘‘In search of a five-point Alexandrov type condition’’
A. Petrunin · 2018
Cited alongside, same era.
‘‘Bipolar comparison’’
N. Lebedeva, A. Petrunin and V. Zolotov · 2019
Cited alongside, same era.
‘‘Curvature and 4-point subspaces’’
N. Lebedeva and V. Zolotov
Cited in the paper.
‘‘5-point CAT ( 0 ) \rm CAT(0) spaces after Tetsu Toyoda’’
N. Lebedeva and A. Petrunin · 2020
Later among the works it cites.
‘‘An intrinsic characterization of five points in a CAT(0) space’’
T. Toyoda · 2020
Later among the works it cites.
‘‘Graph comparison meets Alexandrov’’, 2022
N. Lebedeva and A. Petrunin · 2022
Closest in time.
‘‘Trees meet octahedron comparison’’, 2022
N. Lebedeva and A. Petrunin · 2022
Closest in time.
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