{
  "abstract": "For every admissible non-maximal Toledo invariant $t$, we construct a locus of irreducible representations of a closed genus-$g$ surface group into $\\mathrm{PU}_{2,n+1}$ with Toledo invariant $t$ whose orbit maps are quasi-isometric embeddings. These loci have real codimension $10(g-1)$ or $10(g-1)+2(n-1)$ in the character variety depending on the Toledo value. Our construction uses $4$-cyclic Higgs bundles and their correspondence with $\\partial$-alternating surfaces in complex pseudo-hyperbolic spaces. The associated equivariant minimal maps into the symmetric space are bi-Lipschitz embeddings. We further construct cocompact domains of discontinuity in the Shilov boundary. Their quotients are smooth fiber bundles over the surface with fiber homeomorphic to $S^{2n-1}\\times S^{2n-1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24672",
  "author_total": 2,
  "authors": [
    {
      "name": "Qiongling Li"
    },
    {
      "name": "Junming Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a9hcagykpan4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24672",
  "fulltext_url": null,
  "id": "4a9hcagykpan4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24672",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214031224",
  "pdf_url": "https://arxiv.org/pdf/2609.24672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a9hcagykpan4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.24672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Non-maximal quasi-isometric $\\mathrm{PU}_{2,n+1}$-representations via alternating surfaces in complex pseudo-hyperbolic spaces",
  "title_text": "Non-maximal quasi-isometric PU_2,n+1-representations via alternating surfaces in complex pseudo-hyperbolic spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4a9hcagykpan4",
  "venue": "arXiv",
  "versions": []
}