Speaker
Description
Constraint maps are energy-minimizers under an image constraint, which is a natural vectorial extension of the obstacle problem. These maps develop free boundaries, due to the presence of an obstacle, while they also develop singularities, such as discontinuities, often for topological reasons. The partial regularity theory of these maps was established in the nineties, little has been known concerning their free boundaries. In this talk, I will discuss recent development on the intricate interplay between free boundaries and singularities. This talk is based on a series of joint works with Alessio Figalli (ETH), André Guerra (Cambridge), and Henrik Shahgholian (KTH), as well as recent joint work with Marvin Weidner (U. Bonn) and Hui Yu (NUS).