The Steiner Problem on Closed Surfaces of Constant Curvature
The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region i...
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Format: | Others |
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BYU ScholarsArchive
2015
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Online Access: | https://scholarsarchive.byu.edu/etd/4420 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5419&context=etd |
Summary: | The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface. |
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