Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where
certain equalities are replaced with inequalities. Depending on the signs of the inequalities …

An equidistant decomposition F of a metric space X is a decomposition of X into a collection
of pairwise equidistant closed subsets Li; i 2 I, called the leaves of the decomposition. The …

Some regularity of submetries | Annals of Global Analysis and Geometry Skip to main content
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Abstract Gromov (2001) and Sturm (2003) proved that any four points in a CAT (0) space
satisfy a certain family of inequalities. We call those inequalities the⊠-inequalities, following …

Trees meet octahedron comparison Page 1 arXiv:2212.06445v1 [math.MG] 13 Dec 2022
Trees meet octahedron comparison Nina Lebedeva and Anton Petrunin Abstract We show that …

For any real number κ and any integer n≥ 4, the Cycl n (κ) condition introduced by Gromov
(CAT (κ)-spaces: construction and concentration, Zap. Nauchn. Sem. S.-Peterburg. Otdel …

5-Point CAT(0) Spaces a er Tetsu Toyoda Page 1 Open Access. © 2021 Nina Lebedeva and
Anton Petrunin, published by De Gruyter. This work is licensed under the Creative Commons …

We prove that a Riemannian submersion between smooth, compact, non-negatively curved
Riemannian manifolds has to be smooth, resolving a conjecture by Berestovskii--Guijarro …

For any real number $\kappa $ and any integer $ n\geq 4$, the $\mathrm {Cycl} _n (\kappa)
$ condition introduced by Gromov (2001) is a necessary condition for a metric space to …

Five-Point Toponogov Theorem Page 1 N. Lebedeva and A. Petrunin (2024) “Five-Point
Toponogov Theorem,” International Mathematics Research Notices, Vol. 2024, No. 5, pp …