The Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities

TL;DR

This paper investigates how the spectrum of the Laplacian varies on hyperbolic 3-manifolds with Dehn surgery singularities, depending on the surgery parameters, providing insights into geometric analysis and spectral theory.

Contribution

It introduces a detailed analysis of the Laplacian spectrum on hyperbolic 3-manifolds with Dehn surgery singularities, highlighting the spectral dependence on surgery coefficients.

Findings

Spectrum varies continuously with Dehn surgery parameters

Identification of spectral gaps related to singularity types

Extension of spectral theory to singular hyperbolic manifolds

Abstract

We study the spectrum of the Laplacian on hyperbolic 3-manifolds with Dehn surgery type singularities and its dependence on the generalized Dehn surgery coefficients.