Abstract

We study the low-temperature limit in the Landau-de Gennes theory for liquid crystals. We prove that minimizers under orientable Dirichlet data tend to be almost uniaxial but necessarily contain some biaxiality around the singularities of a limiting harmonic map. In particular we prove that around each defect there must necessarily exist a maximal biaxiality point and a point with a purely uniaxial configuration with a negative order parameter. Estimates for the size of the biaxial cores are also given.

This is joint work with Apala Majumdar and Adriano Pisante.