Surface Nematic Quasi-Uniformity

2025/06/12 by Andrea Pedrini, Pedrini, Andrea, Epifanio G. Virga +1
Engineering · Materials Science · Mathematics · #Advanced Materials and Mechanics #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Liquid Crystal Research Advancements #Mathematical Physics (math-ph) #Soft Condensed Matter (cond-mat.soft)

paper · pdf · doi:10.48550/arxiv.2506.10795

openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the least distorted nematic fields on a generic surface, we relax the notion of uniformity into that of quasi-uniformity and prove that all such fields are parallel transported (in Levi-Civita's sense) by the geodesics of the surface. Both global and local constructions of quasi-uniform fields are presented to illustrate both richness and significance of the proposed notion.

Citations

• Surface Nematic Uniformity
• A Variational Theory for Soft Shells
• Bending-Neutral Deformations of Minimal Surfaces
• Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals
• Dynamic tuning of the director field in liquid crystal shells using block copolymers
• Geometric frustration and compatibility conditions for two dimensional director fields

Related

• Surface Nematic Uniformity
• Structural stability and generic transitions of "incompressible" line fields on surfaces
• Discrete Gradient Line Fields on Surfaces
• Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization
• Rigidity and quasisymmetric uniformization of Thurston-type maps