{
  "abstract": "We study singularities, cut loci and controllability for time-dependent contact Hamilton--Jacobi equations. A contact version of Arnaud's theorem identifies the superdifferential graph of an evolved profile with the contact Hamiltonian image of the differential graph of its positive Lax--Oleinik regularization. This representation defines intrinsic singular characteristics and determines their initial velocity through a minimum-energy selection on the space-time superdifferential. The curves are continuous and locally $1/2$-Hölder, but they need not be locally Lipschitz. The exponent $1/2$ is optimal even for a quadratic Hamiltonian. The intrinsic characteristic issued from a cut point is singular at every later time in the short-time interval. We also establish the contact Lax--Oleinik commutator identities, which identify the superlevel and sublevel sets of the cut time with the corresponding terminal momentum graphs through bi-Lipschitz maps. For reachable terminal data we characterize the associated calibrated sets, and we describe all continuous initial data that reach a prescribed semiconcave profile. The proofs use Herglotz' variational principle and short-time estimates for contact fundamental solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01911",
  "author_total": 3,
  "authors": [
    {
      "name": "Qingyang Cai"
    },
    {
      "name": "Wei Cheng"
    },
    {
      "name": "Tianqi Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axgzb4jrmat60.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01911",
  "fulltext_url": null,
  "id": "axgzb4jrmat60",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01911",
  "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.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axgzb4jrmat60.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Generalized Hamiltonian gradient flow of contact type II: singularities, cut locus, and controllability",
  "title_text": "Generalized Hamiltonian gradient flow of contact type II: singularities, cut locus, and controllability",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/axgzb4jrmat60",
  "venue": "arXiv",
  "versions": []
}