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Shortest Length Geodesics on Closed Hyperbolic Surfaces
(2018-01-31)
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this ...
Compactness Theorems for The Spaces of Distance Measure Spaces and Riemann Surface Laminations
(2018-02-18)
Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the Gromov-Hausdorff distance, is a theorem with many applications. In this thesis, we give a ...