{
  "annotation_id": "e32cfc36-e093-411a-a7c3-8e5ca5b5692f",
  "date_created": "2026-02-17T05:53:24.373000Z",
  "date_modified": "2026-02-17T05:53:24.373000Z",
  "file_hash": "3e4fcd1ff6d9edd82f1bf93ec0392290e7cf53b48d27340f397924e74be4c1c7",
  "private": false,
  "record": {
    "abstract": "In this paper, we establish diameter bounds for compact K\\\"ahler manifolds equipped with K\\\"ahler metrics $\\omega$, assuming the associated measure lies in a specific Orlicz space and satisfies an integrability condition. Firstly, we prove a priori estimates for solutions of the complex Monge-Amp\\`ere equation in Orlicz spaces, encompassing $L^{\\infty}$ and stability estimates. This is achieved by employing Ko{\\l}odziej\u0027s approach \\cite{Ko98} and the argument of Guo-Phong-Tong-Wang \\cite{GuPhToWa21}, respectively. Secondly, building on the work of Guo-Phong-Song-Sturm \\cite{GuPhSoSt24-1}, we derive the uniform (local/global) estimates of the Green\u0027s function and its gradient for the associated K\\\"ahler metric $\\omega$.",
    "arxiv_id": "2601.09893",
    "authors": [
      "Lei Zhang",
      "Zhenlei Zhang"
    ],
    "categories": [
      "math.DG",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Complex Monge-Amp\\`ere equation in Orlicz space and Diameter Bound",
    "url": "https://arxiv.org/abs/2601.09893",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cda36fdc-9b61-4df0-bdfa-a933b1f19fbe",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}