Minimal surfaces in finite volume noncompact hyperbolic 3-manifolds

Collin, Pascal; Hauswirth, Laurent; Mazet, Laurent; Rosenberg, Harold

doi:10.1090/tran/6859

Minimal surfaces in finite volume noncompact hyperbolic $3$-manifolds
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by Pascal Collin, Laurent Hauswirth, Laurent Mazet and Harold Rosenberg PDF

Trans. Amer. Math. Soc. 369 (2017), 4293-4309 Request permission

Corrigendum: Trans. Amer. Math. Soc. 372 (2019), 7521-7524.

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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