Inserted: 21 feb 2021
Last Updated: 21 feb 2021
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of S 2-valued maps defined in cylindrical surfaces, which naturally arises as curved thin-film limit in the theories of nematic liquid crystals and micromagnetics. First, we show that minimal configurations are z-invariant and that energy minimizers in the class of weakly axially symmetric competitors are, in fact, axially symmetric. Our main result is a family of sharp Poincaré-type inequalities, which allow establishing a detailed picture of the energy landscape. Finally, we provide a complete characterization of in-plane minimizers.