Special solutions to Lagrangian mean curvature flow


Yng-Ing Lee 
10:00- 10:50
308 , Mathematics Research Center Building (ori. New Math. Bldg.)

I have been interested in and working on the existence of special Lagrangian/Lagrangian minimal. There are several different approaches we have taken and obtained various results. In recent years, we took the approach of mean curvature flow. Singularities may occur in the flow. They usually model on self-similar solutions and translating solutions. Hence it is very important to study these solutions in studying the singularities. We have constructed many such solutions in a joint work with Joyce, and Tsui. Among our examples, there are three types that are of particular interests. One family is Lagrangian self-expanders that are asymptotic to pair of Lagrangian planes. The Lagrangian angle can be made arbitrarily small, and these examples can serve as local model for surgery. Another family is translating solutions with arbitrarily small Lagrangian angle. Our example is rather surprising and indicates that the flow does not behave well even if under the almost calibrated assumption, which is different from the expectation in the past. Some other families of our examples give external Brakke solutions.