{
  "id": "2210.16376",
  "version": "v1",
  "published": "2022-10-28T19:29:16.000Z",
  "updated": "2022-10-28T19:29:16.000Z",
  "title": "A Heintze--Karcher inequality with free boundaries and applications to capillarity theory",
  "authors": [
    "Matias G. Delgadino",
    "Daniel Weser"
  ],
  "comment": "31 pages, 3 figures, comments welcome!",
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "In this paper we analyze the shape of a droplet inside a smooth container. To characterize their shape in the capillarity regime, we obtain a new form of the Heintze--Karcher inequality for mean convex hypersufaces with boundary lying on curved substrates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-28T19:29:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heintze-karcher inequality",
      "free boundaries",
      "capillarity theory",
      "applications",
      "mean convex hypersufaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}