Tangent lines and torsion of closed space curves

Geometry Topology Working Seminar
Friday, February 25, 2011 - 14:00
2 hours
Skiles 269
Ga Tech
Torsion of a curve in Euclidean 3-space is a quantity which together with the curvature completely determines the curve up to a rigid motion. In this talk we use the curve shortening flow to show that the number of zero torsion points (or vertices) v  a closed space curve c and the number p of the pair of parallel tangent lines of c satisfy the following sharp inequality: v + 2p > 5.