FPM 2013, vol. 18, no. 2, pp. 35-51

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 2, PAGES 35-51

Steiner ratio for the Hadamard surfaces of curvature at most $k < 0$

E. A. Zavalnyuk

Abstract

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In this paper, the Hadamard surfaces of curvature at most $k$ are investigated, which are a particular case of Alexandrov surfaces. It was shown that the total angle at the points of an Hadamard surface is not less than $2$ p. The Steiner ratio of an Hadamard surface was obtained for the case where the surface is unbounded and $k
< 0$ .

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Steiner ratio for the Hadamard surfaces of curvature at most k < 0

Steiner ratio for the Hadamard surfaces of curvature at most $k < 0$