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

Autor:	Collin, Pascal, Hauswirth, Laurent, Mazet, Laurent, Rosenberg, Harold
Rok vydání:	2014
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1405.1324 Zobrazit plný text záznamu View this record from Arxiv