{
  "id": "2411.04959",
  "version": "v1",
  "published": "2024-11-07T18:37:13.000Z",
  "updated": "2024-11-07T18:37:13.000Z",
  "title": "Bounding the dimension of exceptional sets for orthogonal projections",
  "authors": [
    "Peter Cholak",
    "Marianna Csornyei",
    "Neil Lutz",
    "Patrick Lutz",
    "Elvira Mayordomo",
    "D. M. Stull"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "It is well known that if $A\\subseteq\\R^n$ is an analytic set of Hausdorff dimension $a$, then $\\dim_H(\\pi_VA)=\\min\\{a,k\\}$ for a.e. $V\\in G(n,k)$, where $\\pi_V$ is the orthogonal projection of $A$ onto $V$. In this paper we study how large the exceptional set \\begin{center} $\\{V\\in G(n,k) \\mid \\dim_H(\\pi_V A) < s\\}$ \\end{center} can be for a given $s\\le\\min\\{a,k\\}.$ We improve previously known estimates on the dimension of the exceptional set, and we show that our estimates are sharp for $k=1$ and for $k=n-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-07T18:37:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional set",
      "orthogonal projection",
      "hausdorff dimension",
      "analytic set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}