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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
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Length of the transversal for surfaces with cusps
In Peter Buser's Geometry and Spectra of Compact Riemann Surfaces he shows that the length of the transverse curve to a geodesic in a pants decomposition on a compact hyperbolic surface has length a c …