Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 3, pp. 221-227   https://doi.org/10.15407/mag16.03.221     ( to contents , go back )
https://doi.org/10.15407/mag16.03.221

An Estimation of the Length of a Convex Curve in Two-Dimensional Aleksandrov Spaces

Alexander A. Borisenko

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: aborisenk@gmail.com

Received June 2, 2020.

Abstract

In the paper, a generalization of the Toponogov theorem about the length of a curve in a two-dimensional Riemannian manifold is proved for the case of two-dimensional Aleksandrov spaces.

Mathematics Subject Classification 2000: 53C44, 52A40
Key words: $\lambda$-convex curve, two-dimensional Aleksandrov space.

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