Le lemme de Schwarz et la borne sup\'erieure du rayon d'injectivit\'e des surfaces
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Publication:6250815
DOI10.1007/S00229-015-0751-9arXiv1404.4488MaRDI QIDQ6250815
Publication date: 17 April 2014
Abstract: We study the injectivity radius of complete Riemannian surfaces (S,g) with curvature |K(g)| bounded by 1. We show that if S is orientable with nonabelian fundamental group, then there is a point p in S with injectivity radius at least arcsinh(2/sqrt{3}). This lower bound is sharp independently of the topology of S. This result was conjectured by Bavard who has already proved the genus zero cases. We establish a similar inequality for surfaces with boundary. The proofs rely on a version due to Yau of the Schwarz lemma, and on the work of Bavard. This article is the sequel of a previous one where we studied applications of the Schwarz lemma to hyperbolic surfaces.
Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Global Riemannian geometry, including pinching (53C20)
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