On Donaldson’s flow of surfaces in a hyperkähler four-manifold

Abstract

Abstract. We prove some basic properties of Donaldson's flow of surfaces in a hyperkähler 4-manifold. When the initial submanifold is symplectic with respect to one Kähler form and Lagrangian with respect to another, we show that certain kinds of singularities cannot form, and we prove a convergence result under a condition related to one considered by M.-T. Wang for the mean curvature flow.

A priori estimates for Donaldson’s equation over compact Hermitian manifolds

“…For higher dimensional case, Weinkove [23] solved Donaldson's conjecture on a slightly strong condition (1.4) ncχ − (n − 1)ω > 0 using the J-flow. For more detailed discussions and related works, we refer to [4,5,6,7,15,16]. [17,18].…”