Geometry Seminar: F. Litzinger (Otto-von-Guericke-University Magdeburg)

Geometry Seminar (Geometric Analysis)

Speaker: Florian Litzinger (Otto-von-Guericke-University Magdeburg)

Title: Curve shortening flow in high codimension.

Abstract: While the singularity formation of the flow by curvature of curves in the plane is well understood, much less is known about the flow of curves in higher codimension. In particular, closed embedded planar curves stay embedded, eventually become convex and shrink to a round point in finite time, but this is not necessarily the case for curves in codimension two and higher. However, it turns out that these curves in fact become asymptotically planar in the vicinity of a singularity; and combined with a bound on a suitably defined entropy of the inital curve we can show that such curves do become circular and thus shrink to a
point. We will also survey some more recent developments on curve shortening flow in codimensions higher than one.