The Donaldson geometric flow is a local smooth semiflow

Abstract

We prove the local existence of unique smooth solutions of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. It is a semiflow on the Besov space $B^{1,p}_2(M, \Lambda^2)$ for $p > 4$. The Donaldson geometric flow was introduced by Simon Donaldson in [2]. For a detailed exposition see [6].