TL;DR
This paper investigates the stability of Donaldson's hyperk"ahler flow, extending previous results on mean curvature flow stability to a new geometric flow in hyperk"ahler 4-manifolds.
Contribution
It generalizes existing stability theorems from mean curvature flow to Donaldson's hyperk"ahler flow, providing new insights into its dynamic stability.
Findings
Established a dynamic stability theorem for hyperk"ahler flow.
Extended Wang and Tsai's results from mean curvature flow to hyperk"ahler flow.
Demonstrated stability properties in hyperk"ahler 4-manifolds.
Abstract
In this work, we discuss the stability of Donaldson's flow of surfaces in a hyperk\"ahler 4-manifold. In \cite{WT2}, Wang and Tsai proved a uniqueness theorem and dynamic stability theorem of the mean curvature flow for minimal surface. We extend their results and obtain a similar dynamic stability theorem of the hyperk\"ahler flow.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology