When does a curve bound a distorted disk?*

Jack E. Graver, Gerald T. Cargo

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Consider a closed curve in the plane that does not intersect itself; by the Jordan- Schoenflies theorem, it bounds a distorted disk. Now consider a closed curve that intersects itself, perhaps several times. Is it the boundary of a distorted disk that overlaps itself? If it is, is that distorted disk essentially unique? In this paper, we develop techniques for answering both of these questions for any given closed curve in the plane.

Original languageEnglish (US)
Pages (from-to)280-305
Number of pages26
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2011


  • Graphite fragments
  • Immersion

ASJC Scopus subject areas

  • General Mathematics


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