Finite-volume Hyperbolic 3-Manifolds contain immersed Quasi-Fuchsian surfaces

TL;DR

This paper provides a new proof demonstrating that every complete, finite-volume hyperbolic 3-manifold contains an immersed, closed, quasi-Fuchsian surface, advancing understanding of the geometric structures within such manifolds.

Contribution

It introduces a novel proof technique confirming the existence of immersed quasi-Fuchsian surfaces in finite-volume hyperbolic 3-manifolds.

Findings

Existence of immersed quasi-Fuchsian surfaces in all finite-volume hyperbolic 3-manifolds

New proof method for geometric structures in hyperbolic 3-manifolds

Enhanced understanding of surface embeddings in hyperbolic geometry

Abstract

The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.