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Journal Articles Advances in Mathematics Year : 2020

Minimal surfaces near short geodesics in hyperbolic 3-manifolds

Abstract

If M is a finite volume complete hyperbolic 3-manifold, the quantity A_1(M) is defined as the infimum of the areas of closed minimal surfaces in M. In this paper we study the continuity property of the functional A_1 with respect to the geometric convergence of hyperbolic manifolds. We prove that it is lower semi-continuous and even continuous if A_1(M) is realized by a minimal surface satisfying some hypotheses. Understanding the interaction between minimal surfaces and short geodesics in M is the main theme of this paper.
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Dates and versions

hal-01546786 , version 1 (22-08-2022)

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Attribution - NonCommercial

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Harold Rosenberg, Laurent Mazet. Minimal surfaces near short geodesics in hyperbolic 3-manifolds. Advances in Mathematics, 2020, 372, ⟨10.1016/j.aim.2020.107285⟩. ⟨hal-01546786⟩
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