{
  "annotation_id": "ab3a85f4-dddc-412e-aba2-7c0398db97f3",
  "date_created": "2026-02-17T05:53:16.232000Z",
  "date_modified": "2026-02-17T05:53:16.232000Z",
  "file_hash": "776c4f250c7f933349661d8a7ec116bd74b13c9d054d5320c8988f33c98753c0",
  "private": false,
  "record": {
    "abstract": "We obtain effective estimates for the growth rate of the $L^2$-energy of harmonic functions on geodesic balls in complete simply connected non-positively curved Riemannian manifolds with pinched sectional curvature. Our study relies upon a double-sided Price inequality for harmonic functions. Finally, we apply this circle of ideas to study the analytical structure of a potential counterexample to the Singer conjecture in degree one.",
    "arxiv_id": "2601.08804",
    "authors": [
      "Luca F. Di Cerbo",
      "Hayden Hunter",
      "Aaron K. Thrasher"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds",
    "url": "https://arxiv.org/abs/2601.08804",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "73b6757c-996a-4af7-be77-b3339fec6031",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}