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BIRS Workshop Lecture Videos

Symmetry and multiple existence of critical points in 2D Landau-de Gennes Q-tensor theory Nguyen, Luc


We study a Laudau-de Gennes model for liquid crystals where both the energy functional and the boundary data are invariant under the orthogonal group. In three dimensional settings, it is conjectured that minimizers break the rotational symmetry. We show however that in two dimensional settings, this no longer holds when the boundary data have no topological obstruction: the minimizers are `unique and rotationally symmetric'. As an application, we obtain existence of (multiple) non-minimizing rotationally symmetric critical points. Joint work with Radu Ignat, Valeriy Slastikov and Arghir Zarnescu.

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