Filling multiples of embedded curves
Time and place
1 PM on Thursday, October 23rd, 2014; NAC 6/113
Robert Young (NYU)
Abstract
One of the motivating questions of geometric measure theory involves filling area, the minimal area of an oriented surface whose boundary is a given curve. There are still open questions about filling area even in the classical case of curves in R^n. For example, filling a curve with an oriented surface can sometimes be "cheaper by the dozen" --- L. C. Young constructed a smooth curve drawn on a projective plane in R^n which is only about 1.3 times as hard to fill twice as it is to fill once and asked whether this ratio can be bounded below. We will answer this question and pose some open questions about surfaces embedded in R^n.
