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arXiv · 1404.4487

Trois applications du lemme de Schwarz aux surfaces hyperboliques

Matthieu Gendulphe
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Abstract

Through the Schwarz lemma, we provide a new point of view on three well-known results of the geometry of hyperbolic surfaces. The first result deal with the length of closed geodesics on hyperbolic surfaces with boundary (Thurston, Parlier, Papadopoulos-Th\'eret). The two others give sharp lower bounds on two metric invariants: the length of the shortest non simple closed geodesic, and the radius of the biggest embedded hyperbolic disk (Yamada). We also discuss a question of Papadopoulos and Th\'eret about the length of arcs on surfaces with boundary. In a sequel, we use a generalization of the Schwarz lemma due to Yau to study the injectivity radius of surfaces with bounded curvature.

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Matthieu Gendulphe. 2014-04-17. Trois applications du lemme de Schwarz aux surfaces hyperboliques. https://arxiv.org/abs/1404.4487

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