OPTIMAL MORSE-SMALE FLOWS WITH SINGULARITIES ON THE BOUNDARY OF A SURFACE

摘要

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 Moebius strip, on a torus with hole, and on a Klein bottle with hole.