Hyperbolic Eisenstein series for geometrically finite hyperbolic surfaces of infinite volume

TL;DR

This paper develops a spectral decomposition for the Laplacian on 1-forms on infinite volume hyperbolic surfaces and generalizes the construction of hyperbolic Eisenstein series, expanding understanding of spectral theory in this context.

Contribution

It introduces a spectral decomposition for the Laplacian on 1-forms and generalizes hyperbolic Eisenstein series construction for geometrically finite infinite volume surfaces.

Findings

Spectral decomposition for Laplacian on 1-forms established

Generalization of hyperbolic Eisenstein series constructed

Related spectral results extended to infinite volume surfaces

Abstract

For a geometrically finite hyperbolic surface of infinite volume we write down the spectral decomposition for the Laplacian on 1-forms, generalize the Kudla and Millson's construction of hyperbolic Eisenstein series and other related results.