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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Logan, Andrew, "The Steiner Problem on Closed Surfaces of Constant Curvature" (2015). All Theses and Dissertations. 4420.
Steiner problem, Riemannian manifold, closed surfaces of constant curvature