{
  "abstract": "We present a unified approach to proving the following two results: (i) Let $G$ be a Lie group, $Γ$ a lattice in $G$, $X=G/Γ$, and let $F$ be a one-parameter $\\mathrm{Ad}$-diagonalizable subgroup of $G$. Then the set $$ \\{x\\in X:Fx\\text{ is bounded in }X\\} $$ is hyperplane absolute winning on $X$. This fully solves a conjecture [Conjecture 7.1]{AGK} of An-Guan-Kleinbock in 2015. (ii) Let $G$ be a connected semisimple Lie group with finite center and without compact factors, $K\\leq G$ a maximal compact subgroup, $Γ\\leq G$ a torsion-free lattice, and $M=K\\backslash G/Γ$. Then for any $p\\in M$, the set $$\\{ξ\\in S_pM:γ(p,ξ)\\text{ is bounded in }M\\}$$ is hyperplane absolute winning on $S_pM$, where $γ(p,ξ)$ denotes the geodesic ray through the base point $p$ in the direction $ξ$. This fully solves a conjecture [Conjecture 1.2]{GW26} of Guan-Wu in 2026.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24979",
  "author_total": 1,
  "authors": [
    {
      "name": "Chengyang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axs7yr4vm9yg2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24979",
  "fulltext_url": null,
  "id": "axs7yr4vm9yg2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24979",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223016595",
  "pdf_url": "https://arxiv.org/pdf/2610.24979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axs7yr4vm9yg2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Bounded orbits on homogeneous spaces and bounded geodesics on locally symmetric spaces",
  "title_text": "Bounded orbits on homogeneous spaces and bounded geodesics on locally symmetric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/axs7yr4vm9yg2",
  "venue": "arXiv",
  "versions": []
}