Spectral Gaps on Large Hyperbolic Surfaces
Laura Monk, Fr\'ed\'eric Naud
TL;DR
This paper reviews recent advances in the spectral theory of large hyperbolic surfaces, focusing on the behavior of the first non-trivial eigenvalue as the surface volume increases.
Contribution
It provides an overview of the history and recent breakthroughs concerning the spectral properties of large hyperbolic surfaces, emphasizing eigenvalue behavior.
Findings
Summary of historical developments in spectral theory
Recent results on eigenvalue bounds for large hyperbolic surfaces
Insights into the behavior of the first non-trivial eigenvalue
Abstract
In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the investigation of the first non-trivial eigenvalue and its possible behaviour in the large volume regime.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · Analytic Number Theory Research