{
  "abstract": "Let $M=\\mathbb{H}^2\\times\\mathbb{T}$ carry its product metric. We prove that the Schrödinger evolution maps $L^2(\\mathbb{H}^2;H^s(\\mathbb{T}))$ into $L^2([0,1];L^6(M))$ for every $s>0$, without any regularity assumption in the hyperbolic variable. The proof separates hyperbolic and periodic frequencies. A localized hyperbolic kernel estimate restricts the effective interaction time at hyperbolic frequency $L$ to order $L^{-1}$. Quadratic exponential sums then give a logarithmic bound when the periodic bandwidth is comparable to $L$. A mixed-norm decoupling argument, including an $L^6$-valued extension and a periodic transference step, reduces wider periodic bands to this case. The infimum of the admissible periodic regularities is therefore zero. The estimate at zero regularity is not established here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27920",
  "author_total": 1,
  "authors": [
    {
      "name": "Xuyi Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aas2ddnr7t0ap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27920",
  "fulltext_url": null,
  "id": "aas2ddnr7t0ap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27920",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223097837",
  "pdf_url": "https://arxiv.org/pdf/2610.27920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aas2ddnr7t0ap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Schrödinger estimates with arbitrarily small periodic regularity on $\\mathbb{H}^2 \\times \\mathbb{T}$",
  "title_text": "Schrödinger estimates with arbitrarily small periodic regularity on ℍ^2 × 𝕋",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/aas2ddnr7t0ap",
  "venue": "arXiv",
  "versions": []
}