{
  "abstract": "Let $S$ be a closed oriented surface of genus at least $2$. Let $X$ be a $(2,1)$-dimensional anti-de Sitter spacetime homeomorphic to $S\\times[-1,1]$ with smooth, spacelike, strongly convex boundary. By Gauss' formula, the induced metric on each of the two components of $\\partial X$ has curvature $K<-1$. In this paper we address the inverse problem. We show that, for any two smooth metrics $h_-, h_+$ on $S$ with curvature $K<-1$, there exists a unique, smooth anti-de Sitter metric on $X:=S\\times [-1,1]$ with respect to which the boundary is locally strongly convex and has induced metric isotopic to $h_-$ on its past component and isotopic to $h_+$ on its future component. Existence has already been proven by Tamburelli. We use this result to solve affirmatively a conjecture of Mess: given any two measured laminations $l_-, l_+\\in\\mathcal{ML}_S$ that together fill $S$, there exists a unique $(2,1)$-dimensional, globally hyperbolic, maximal, Cauchy compact (GHMC) anti-de Sitter spacetime such that the measured bending laminations of the past and future boundary components of its convex core are respectively $l_-$ and $l_+$. Here, existence has already been proven by Bonsante--Schlenker.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05506",
  "author_total": 3,
  "authors": [
    {
      "name": "Roman Prosanov"
    },
    {
      "name": "Jean-Marc Schlenker"
    },
    {
      "name": "Graham Andrew Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3s4fm9fx688mh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05506",
  "fulltext_url": null,
  "id": "3s4fm9fx688mh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05506",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220703339",
  "pdf_url": "https://arxiv.org/pdf/2610.05506",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3s4fm9fx688mh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05506",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05506"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On $(2,1)$-dimensional anti-de Sitter spacetimes with convex boundary",
  "title_text": "On (2,1)-dimensional anti-de Sitter spacetimes with convex boundary",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:26Z",
  "url": "https://research.draconitic.com/paper/3s4fm9fx688mh",
  "venue": "arXiv",
  "versions": []
}