Analysis of variational model for nematic shells

In this talk, I will introduce and analyse an elastic

surface energy recently introduced by G. Napoli and

L. Vergori to model thin films of nematic liquid crystals.

As it will be clear, the topology and the geometry of

the surface will play a fundamental role in understanding

the behavior of thin films of liquid crystals.

In particular, our results regards the existence of

minimizers, the existence of the gradient flow

of the energy and, in the case of an axisymmetric

toroidal particle, a detailed characterization of global and local minimizers.

This last item is supplemented with numerical experiments.

This is a joint work with M. Snarski (Brown) and M. Veneroni (Pavia).