When Does a Curve Bound a Distorted Disk?

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.      dd dd Three of these curves bound distorted disks; one does not. Also, one of the three bounds two distinct distorted disks. 1 

• Type: Journal
• Year: 2011
• Where: SIAMDM
• Authors: Jack E. Graver, Gerald T. Cargo
• Keywords: Closed Curve, Distorted, Distorted Disks, SIAMDM 2011, Software Engineering