@article{Fratta2023, 
author = {Giovanni Di Fratta and Alberto Fiorenza and Valeriy Slastikov},
title = {On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {3},
pages = {1-38},
keywords = {Poincaré inequality, harmonic maps, magnetic skyrmions},
url = {https://www.sciopen.com/article/10.3934/mine.2023056},
doi = {10.3934/mine.2023056},
abstract = {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. The model naturally arises as a curved thin-film limit in the theories of nematic liquid crystals and micromagnetics. 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 inequality on the circular cylinder, which allows for establishing a nearly complete picture of the energy landscape. The presence of symmetry-breaking phenomena is highlighted and discussed. Finally, we provide a complete characterization of in-plane minimizers, which typically appear in numerical simulations for reasons we explain.}
}