{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37573",
  "author_total": 3,
  "authors": [
    {
      "name": "Alex Cohen"
    },
    {
      "name": "Zhenhao Li"
    },
    {
      "name": "Zhongkai Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e583qvtf1s04t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37573",
  "fulltext_url": null,
  "id": "e583qvtf1s04t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37573",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
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  ],
  "openalex": "W7224105259",
  "pdf_url": "https://arxiv.org/pdf/2610.37573",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e583qvtf1s04t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37573",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37573"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Escape of mass for finite-area hyperbolic surfaces",
  "title_text": "Escape of mass for finite-area hyperbolic surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/e583qvtf1s04t",
  "venue": "arXiv",
  "versions": []
}