Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 3, pp. 221-227     ( to contents , go back )

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

Received June 2, 2020.


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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