Analysis Seminar

Filippo GaiaETH Zurich
Singularities of Hamiltonian Stationary Lagrangian Surfaces

Wednesday, February 19, 2025 - 2:30pm
Malott 203

I will discuss the existence and regularity of critical points of the area functional among Lagrangian surfaces in symplectic 4-manifolds, reviewing classical results by R. Schoen and J. Wolfson and recent progress by A. Pigati and T. Rivière. I will then present a variational construction of Hamiltonian stationary Lagrangian immersions in C^2 with multiple singularities at prescribed points, based on the sharp Wente inequality and an asymptotic analysis at the singularities. This is based on joint work with G. Orriols and T. Rivière.