Optimal Morse–Smale Flows with Singularities on the Boundary of a Surface

Abstract

We consider the optimal flows on noncompact surfaces with boundary, which have a minimum number of fixed points and all these points lie on the boundary of the surface. It is proved that the flow is optimal if it has a single sink and a single source. We describe the structures of the optimal flows on a simply connected region, on a Mobius strip, on a torus with hole, and on a Klein bottle with hole.