Evolution by mean curvature flow of Lagrangian spherical surfaces in complex Euclidean plane

Abstract

We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane $\mathbb{C}^2$. In particular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves about finding out a condition on a starting Lagrangian torus in $\mathbb{C}^2$ such that the corresponding mean curvature flow becomes extinct at finite time and converges after rescaling to the Clifford torus.

13 pages. This new version includes drafting changes in some points to make the paper more readable and the deletion of the old Theorem B because the proof was incomplete. Accepted in Journal of Mathematical Analysis and Applications