Abstract:

The hyper-Kaehler Flow was first studied by Donaldson. Later Song and Weinkove gave a more complete result for this flow. They show the connection between mean curvature flow and hyper-Kaehler flow. I will briefly introduce hyper-Kaehler flow and discuss in the special case its similarity to the Lagrangian mean curvature flow. Finally I will prove a long time existence result in the Eguchi-Hanson space.