{
  "id": "2002.10141",
  "version": "v1",
  "published": "2020-02-24T10:13:47.000Z",
  "updated": "2020-02-24T10:13:47.000Z",
  "title": "Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains",
  "authors": [
    "Kazuhiro Ishige",
    "Paolo Salani",
    "Asuka Takatsu"
  ],
  "comment": "24 pages. Comments are welcome!",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study power concavity of rotationally symmetric solutions to elliptic and parabolic boundary value problems on rotationally symmetric domains in Riemannian manifolds. As applications of our results to the hyperbolic space ${\\bf H}^N$ we have: $\\bullet$ The first Dirichlet eigenfunction on a ball in ${\\bf H}^N$ is strictly positive power concave; $\\bullet$ Let $\\Gamma$ be the heat kernel on ${\\bf H}^N$. Then $\\Gamma(\\cdot,y,t)$ is strictly log-concave on ${\\bf H}^N$ for $y\\in {\\bf H}^N$ and $t>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-24T10:13:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J32",
      "52A55"
    ],
    "keywords": [
      "parabolic boundary value problems",
      "rotationally symmetric domains",
      "study power concavity",
      "first dirichlet eigenfunction",
      "symmetric solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}