{
  "annotation_id": "28904605-9ea6-4396-83cc-957c6ff49498",
  "date_created": "2026-02-17T05:53:12.489000Z",
  "date_modified": "2026-02-17T05:53:12.489000Z",
  "file_hash": "a081ef1af23f21ab70286591378642747baeff3f91daf7daa0c021cfc7f1c50e",
  "private": false,
  "record": {
    "abstract": "Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a K\\\"ahler metric $\\omega$ and a closed $(1, 1)$-form $\\alpha$. Assuming a uniform estimate for $\\omega$, we prove higher order estimates and smooth convergence to a cscK metric coupled to a harmonic $(1, 1)$-form. A simplification of the system is used to recover existence results for K\\\"ahler-Einstein metrics when $c_1(X) \u003c 0$. On Riemann surfaces with genus at least $2$, we show smooth convergence to the unique K\\\"ahler-Einstein metric from a large class of initial data.",
    "arxiv_id": "2601.07677",
    "authors": [
      "Xi Sisi Shen",
      "Kevin Smith"
    ],
    "categories": [
      "math.DG",
      "math.AP",
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Coupled continuity equations for constant scalar curvature K\\\"ahler metrics",
    "url": "https://arxiv.org/abs/2601.07677",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "955fe02a-4436-416f-8044-9b8c4c4dd5dd",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}