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.References
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Additional Information
- Pascal Collin
- Affiliation: Institut de mathematiques de Toulouse, Université Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse cedex, France
- MR Author ID: 294252
- Email: collin@math.ups-tlse.fr
- Laurent Hauswirth
- Affiliation: Université Paris-Est, LAMA (UMR 8050), UPEM, UPEC, CNRS, F-77454, Marne-la-Vallee, France
- MR Author ID: 649999
- Email: hauswirth@univ-mlv.fr
- Laurent Mazet
- Affiliation: Université Paris-Est, LAMA (UMR 8050), UPEC, UPEM, CNRS, 61, avenue du Général de Gaulle, F-94010 Créteil cedex, France
- MR Author ID: 722767
- Email: laurent.mazet@math.cnrs.fr
- Harold Rosenberg
- Affiliation: Instituto Nacional de Matematica Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro-RJ, Brazil
- MR Author ID: 150570
- Email: rosen@impa.br
- Received by editor(s): August 19, 2015
- Received by editor(s) in revised form: September 19, 2015
- Published electronically: February 23, 2017
- Additional Notes: The authors were partially supported by grant ANR-11-IS01-0002.
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 4293-4309
- MSC (2010): Primary 53A10
- DOI: https://doi.org/10.1090/tran/6859
- MathSciNet review: 3624410