{
  "abstract": "We study regularity of bounded weak solutions to complex Monge-Amp{è}re equations on compact Hermitian manifolds with right-hand side possibly decreasing in the unknown. Our proof relies on the domination principle and a priori estimates, partially motivated by the Monge-Amp{è}re eigenvalue problem. Our main result roughly says that any bounded solution is smooth in the regular locus of the data. When the right-hand side is strictly positive and smooth, we recover known results by Nie, Ko lodziej-Nguyen for the Hermitian case and Sz{é}kelyhidi-Tosatti for the K{ä}hler case, which rely on the regularizing property of the K{ä}hler-Ricci flow.",
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  "article_type": null,
  "arxiv": "2610.06473",
  "author_total": 3,
  "authors": [
    {
      "name": "Papa Badiane"
    },
    {
      "name": "Chinh H. Lu"
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    {
      "name": "Ahmed Zeriahi"
    }
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  "bibtex": "https://research.draconitic.com/paper/5rpd1tma0x2kn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06473",
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  "pdf_url": "https://hal.science/hal-05776079/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5rpd1tma0x2kn.ris",
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      "first_seen": "2026-10-30T12:17:46Z",
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      "native_id": "2610.06473",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06473"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
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  ],
  "title": "Complex Monge-Ampère equations on Hermitian Manifolds: From bounded to smooth solutions",
  "title_text": "Complex Monge-Ampère equations on Hermitian Manifolds: From bounded to smooth solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/5rpd1tma0x2kn",
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}