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.
Domains
Differential Geometry [math.DG]| Origin | Files produced by the author(s) |
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