{
  "annotation_id": "d740b5c0-f251-4d22-a8d2-39323d88f292",
  "date_created": "2026-02-17T05:53:19.957000Z",
  "date_modified": "2026-02-17T05:53:19.957000Z",
  "file_hash": "9bbb589de25b5063c0cabadbe401a24d46174b321155f589db1b0247e7c21c0e",
  "private": false,
  "record": {
    "abstract": "In this paper we study some relationships between the first Dirichlet eigenvalue $\\Lambda(\\Omega)$ and the torsional rigidity $T(\\Omega)$ of a domain $\\Omega$. We consider the problem of optimizing the product $\\Lambda(\\Omega)T(\\Omega)$ among sets with prescribed perimeter, both in the class of open sets with finite perimeter and within the class of convex domains.\n  We also present local results for the quantity $\\Lambda(\\Omega)T(\\Omega)^q$, with $q\u003e0$, under either a volume or a perimeter constraint.",
    "arxiv_id": "2601.09592",
    "authors": [
      "Vincenzo Amato",
      "Carlo Nitsch",
      "Cristina Trombetti",
      "Federico Villone"
    ],
    "categories": [
      "math.SP",
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On some functionals involving torsional rigidity, principal eigenvalue and perimeter",
    "url": "https://arxiv.org/abs/2601.09592",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ddcbd375-76cc-4664-840a-48aca5b60a98",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}