The Bao—Ratiu equations on surfaces
Bennett Palmer · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1995
Abstract We study the existence of asymptotic directions for the volume preserving diffeomorphism group of a compact surface Ʃ, considered as a submanifold of the full diffeomorphism group. We show that when the curvature of Ʃ is positive, there are no asymptotic directions. Related results are obtained for domains with boundary.