{
  "id": "2310.03683",
  "version": "v1",
  "published": "2023-10-05T17:01:51.000Z",
  "updated": "2023-10-05T17:01:51.000Z",
  "title": "A strong min-max property for level sets of Phase Transitions",
  "authors": [
    "Érico Melo Silva"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that certain functions whose nodal sets lie near a fixed nondegenerate minimal hypersurface satisfy a strong min-max principle for the Allen--Cahn energy which is analogous to the strong min-max principle for non-degenerate minimal hypersurfaces first proved by Brian White.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T17:01:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strong min-max property",
      "level sets",
      "phase transitions",
      "strong min-max principle",
      "non-degenerate minimal hypersurfaces first"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}