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arXiv · 2610.37573

Escape of mass for finite-area hyperbolic surfaces

Alex Cohen·Zhenhao Li·Zhongkai Tao
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Abstract

Let $M$ be a noncompact finite-area hyperbolic surface. We give a lower bound for the $L^2$ norm of eigenfunctions and Eisenstein series in a compact part of the surface. This extends a result of Soundararajan [arXiv:0901.4060] to the nonarithmetic setting. The crucial components of the proof are a long-time Egorov's theorem designed for this setting, a nonlinear uncertainty principle of Cohen--Dyatlov [arXiv:2609.30261], and an application of Weyl's method for exponential sums.

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Alex Cohen, Zhenhao Li, Zhongkai Tao. 2026-10-27. Escape of mass for finite-area hyperbolic surfaces. https://arxiv.org/abs/2610.37573

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