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arXiv · 1404.4488

Le lemme de Schwarz et la borne supérieure du rayon d'injectivité des surfaces

Matthieu Gendulphe
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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.

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Matthieu Gendulphe. 2014-04-17. Le lemme de Schwarz et la borne supérieure du rayon d'injectivité des surfaces. https://arxiv.org/abs/1404.4488

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