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.
“…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].…”
In this paper we prove a priori estimates for Donaldson's equationover a compact complex manifold X of complex dimension n, where ω and χ are arbitrary Hermitian metrics. Our estimates answer a question of Tosatti-Weinkove in [17].
“…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].…”
In this paper we prove a priori estimates for Donaldson's equationover a compact complex manifold X of complex dimension n, where ω and χ are arbitrary Hermitian metrics. Our estimates answer a question of Tosatti-Weinkove in [17].
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