{
  "abstract": "In this paper we study coupled constant scalar curvature Kähler metrics defined by Datar-Pingali extending coupled Kähler-Einstein metrics defined by Hultgren-Witt Nyström. We consider two K-energy functionals of which one (denoted $\\mathcal{M}_{\\operatorname{ccscK}}$) integrates the moment map considered by Datar-Pingali and the other (denoted $\\mathcal{M}'$) is designed so that its slope at infinity for subgeodesic rays for ample test configurations with reduced central fiber coincides with the Donaldson-Futaki invariant considered by Hultgren-Witt Nyström and Datar-Pingali. We also extend $\\mathcal{M}_{\\operatorname{ccscK}}$ to $\\mathcal{H}^{1,\\bar{1}}$ and the finite energy class $\\mathcal{E}^1$, and prove its convexity along tuples of weak geodesics and finite energy geodesics, respectively. As a corollary, we obtain a semistability condition necessary for the existence of ccscK metrics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34145",
  "author_total": 2,
  "authors": [
    {
      "name": "Akito Futaki"
    },
    {
      "name": "Jianwei Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecmyw4mkavy9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34145",
  "fulltext_url": null,
  "id": "ecmyw4mkavy9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34145",
  "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"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223941461",
  "pdf_url": "https://arxiv.org/pdf/2610.34145",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecmyw4mkavy9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34145",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34145"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "K-energy for the coupled constant scalar curvature Kähler equation, I: Slope formula and semistability",
  "title_text": "K-energy for the coupled constant scalar curvature Kähler equation, I: Slope formula and semistability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ecmyw4mkavy9s",
  "venue": "arXiv",
  "versions": []
}