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Journal Articles Transactions of the American Mathematical Society Year : 2017

Minimal surfaces in finite volume non compact hyperbolic $3$-manifolds

Abstract

We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic $3$-manifold $\mathcal{N}$. We also obtain a least area, incompressible, properly embedded, finite topology, $2$-sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This determines its asymptotic behavior. Some rigidity theorems are obtained.
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Dates and versions

hal-01015056 , version 1 (16-12-2022)

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Pascal Collin, Laurent Hauswirth, Laurent Mazet, Harold Rosenberg. Minimal surfaces in finite volume non compact hyperbolic $3$-manifolds. Transactions of the American Mathematical Society, 2017, 369 (6), pp.4293-4309. ⟨10.1090/tran/6859⟩. ⟨hal-01015056⟩
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