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 -manifolds

Authors: Pascal Collin, Laurent Hauswirth, Laurent Mazet and Harold Rosenberg
Journal: Trans. Amer. Math. Soc. 369 (2017), 4293-4309
MSC (2010): Primary 53A10
DOI: https://doi.org/10.1090/tran/6859
Published electronically: February 23, 2017
Corrigendum: Trans. Amer. Math. Soc. 372 (2019), 7521-7524.
MathSciNet review: 3624410
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Abstract: We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic -manifold $\mathcal {N}$ . We also obtain a least area, incompressible, properly embedded, finite topology, -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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