CURVE SHORTENING ON SASAKI MANIFOLDS AND THE WEINSTEIN CONJECTURE

摘要

We propose a new geometric evolution equation for closed curves on contact manifolds. Our flow is a parabolic evolution equation similar to the well known curve shortening flow (mean curvature flow) and is the negative gradient flow of the Reeb energy of closed curves. We analyze the longtime arid singular behavior of the flow and describe relations to the Weinstein conjecture on the existence of closed Reeb orbits.