{
  "id": "2212.09954",
  "version": "v1",
  "published": "2022-12-20T02:03:30.000Z",
  "updated": "2022-12-20T02:03:30.000Z",
  "title": "Singularities of Fitzpatrick and convex functions",
  "authors": [
    "Dmitry Kramkov",
    "Mihai Sîrbu"
  ],
  "comment": "21 pages, submitted",
  "categories": [
    "math.CA"
  ],
  "abstract": "Zaj\\'{\\i}\\v{c}ek [19] shows that the singularities of a convex function $f$ can be covered by a countable collection of $c-c$ surfaces. We study the geometry of these surfaces and show that their normals are restricted to the cone generated by $F-F$, where $F:= \\textrm{cl} \\ \\textrm{range} \\nabla f$. The singularities of projections on monotone sets in pseudo-Euclidean spaces and of the associated Fitzpatrick functions are studied and classified as a case of special interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-20T02:03:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex function",
      "singularities",
      "monotone sets",
      "pseudo-euclidean spaces",
      "associated fitzpatrick functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}