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We describe the evolution under the mean curvature flow of embeddedLagrangian spherical surfaces in the complex Euclidean plane $\mathbb{C}^2$. Inparticular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves aboutfinding out a condition on a starting Lagrangian torus in $\mathbb{C}^2$ suchthat the corresponding mean curvature flow becomes extinct at finite time andconverges after rescaling to the Clifford torus.

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