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

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

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...

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Veröffentlicht in:Transactions of the American Mathematical Society 2017, Vol.369 (6)
Hauptverfasser: Collin, Pascal, Hauswirth, Laurent, Mazet, Laurent, Rosenberg, Harold
Format: Artikel
Sprache:eng
Schlagworte:
Differential Geometry
Mathematics
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6859