{
  "abstract": "This paper is the continuation of our earlier work on Holder estimates for Kahler potentials on compact normal Kahler spaces. We establish a geometric counterpart for analytic Holder regularity of Kolodziej. If a singular metric $ω_ϕ$ has Holder continuous potentials with respect to a smooth background metric, then its distance function is Holder continuous with respect to a smooth background distance. The result holds on normal Kahler spaces and yields compactness of the metric completion as well as its identification with the underlying complex space if $ω_ϕ$ is a Kahler current. Under this positivity assumption, our estimates establish the Holder equivalence between the intrinsic canonical Kahler metrics and the extrinsic smooth metrics on Kahler-RCD spaces, particularly on smoothable Kahler-Einstein spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28982",
  "author_total": 3,
  "authors": [
    {
      "name": "Bin Guo"
    },
    {
      "name": "Jian Song"
    },
    {
      "name": "Jacob Sturm"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxn68pe804n6j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28982",
  "fulltext_url": null,
  "id": "fxn68pe804n6j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28982",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214294883",
  "pdf_url": "https://arxiv.org/pdf/2609.28982",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxn68pe804n6j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28982",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28982"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Geometric Holder estimates for complex Monge-Ampere equations",
  "title_text": "Geometric Holder estimates for complex Monge-Ampere equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/fxn68pe804n6j",
  "venue": "arXiv",
  "versions": []
}