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Steiner Trees on Curved Surfaces

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Abstract.

 The Steiner tree problem on surfaces is more complicated than the corresponding one in the Euclidean plane. There are not many results on it to date. In this paper we first make a comparison of Steiner minimal trees on general curved surfaces with Steiner minimal trees in the Euclidean plane. Then, we focus our study on the Steiner trees on spheres. In particular, we detail the properties of locally minimal Steiner points, and the Steiner points for spherical triangles.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, and Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3052, Australia e-mail: weng@ms.unimelb.edu.au, , , , , , AU

    J. F. Weng

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  1. J. F. Weng
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Received: August 18, 1997 Final version received: March 16, 1998

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Weng, J. Steiner Trees on Curved Surfaces. Graphs Comb 17, 353–363 (2001). https://doi.org/10.1007/PL00007249

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  • DOI: https://doi.org/10.1007/PL00007249

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