{
  "annotation_id": "4a350c13-9e81-4fc9-95dc-48174333c5ea",
  "date_created": "2026-02-17T05:53:12.656000Z",
  "date_modified": "2026-02-17T05:53:12.656000Z",
  "file_hash": "b72ac289a75f06613b67000eed8c44ecec711dfb986cc12249d4786839b3f86f",
  "private": false,
  "record": {
    "abstract": "We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends on the underlying domain only through very simple geometric characteristics. This is proved via a precise and uniform expansion of the on-diagonal heat kernel close to the boundary. Most of our results are valid without the convexity assumption and we also consider two-term asymptotics for the heat trace for Lipschitz domains.",
    "arxiv_id": "2601.07341",
    "authors": [
      "Rupert L. Frank",
      "Simon Larson"
    ],
    "categories": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Uniform bounds for Neumann heat kernels and their traces in convex sets",
    "url": "https://arxiv.org/abs/2601.07341",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e7da190b-b494-4fb7-93a9-d878ac457142",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}