Orateur
Dominik Stantejsky
Description
Motivated by experiments with nematic liquid crystal droplets, we study harmonic maps on the three-dimensional unit ball that arise as minimizers of the one-constant approximation of the Oseen-Frank energy subject to strong anchoring planar boundary condition. Through a reflection method, we are able to study regularity of minimizers close to the boundary. We also obtain results on the type and location of defects that can occur, such as boundary ``boojums'' and interior vortices. The talk is based on joint work with Lia Bronsard and Andrew Colinet.