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The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
Theses and Dissertations
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.