Minimal Surfaces in Hyperbolic 3-manifolds

Abstract

In this paper, we show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic $3$-manifolds except some special cases.

Tube Lemma removed, and proof simplified. New figures added

References in corpus (3)

• Tameness of hyperbolic 3-manifolds
• Existence of infinitely many minimal hypersurfaces in closed manifolds
• A dichotomy for minimal hypersurfaces in manifolds thick at infinity

Cited by in corpus (3)

• A dichotomy for minimal hypersurfaces in manifolds thick at infinity
• The Allen-Cahn equation on the complete Riemannian manifolds of finite volume
• Beyond almost Fuchsian space