{
  "annotation_id": "8f5f6ff3-9883-4662-9b82-bb13962d4841",
  "date_created": "2026-02-17T05:53:12.550000Z",
  "date_modified": "2026-02-17T05:53:12.550000Z",
  "file_hash": "86db1642912b1fb0141bfdd9239d5d3002388b06eed913eade97774eba31183d",
  "private": false,
  "record": {
    "abstract": "In this paper, we investigate the log-concavity of the kernel for the parabolic Ornstein-Uhlenbeck operator in a bounded, convex domain. Consequently, we get the preservation of the log-concavity of the initial datum by the related flow. As an application, we give another proof of a Brunn-Minkowski type inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and of the log-concavity of the related first eigenfunction (both results have been proved in [9], by different methods).",
    "arxiv_id": "2601.07426",
    "authors": [
      "Andrea Colesanti",
      "Lei Qin",
      "Paolo Salani"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Log-concavity of solutions of parabolic equations related to the Ornstein-Uhlenbeck operator and applications",
    "url": "https://arxiv.org/abs/2601.07426",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b373bb4d-90a3-4033-8b8a-1426f1f94cb6",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}