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Steiner Ratio for Hadamard Surfaces of Curvature at Most k < 0

Abstract

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 2π. The Steiner ratio of an Hadamard surface was obtained for the case where the surface is unbounded and k < 0.

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Correspondence to E. Zavalnyuk.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 35–51, 2013.

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Zavalnyuk, E. Steiner Ratio for Hadamard Surfaces of Curvature at Most k < 0. J Math Sci 203, 777–788 (2014). https://doi.org/10.1007/s10958-014-2167-6

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Keywords

  • Short Path
  • Riemannian Manifold
  • Minimal Span Tree
  • Steiner Tree
  • Euclidean Plane