| Contents |
| In this talk and in the subsequent Part B, we discuss some features of a newly proposed variational
model for nematic shells, which consist in a thin film of liquid crystals coating a particle.
In particular, we consider a surface energy, recently proposed by G. Napoli and L. Vergori, which
exhibits a combination of effects related both to intrinsic and extrinsic geometric quantities.
The aim of this talk is to present some results about the existence of equilibrium configurations for substrates with genus $1$. Moreover, we will discuss also the evolution of the energy along a gradient flow.
Particular emphasis will be given in explaining how the topology and the geometry of the surface influence the existence and the behaviour of the equilibrium configurations. |
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