2006/01/20 by Randall D. Kamien, Christian D. Santangelo · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Liquid Crystal Research Advancements #Mathematical Dynamics and Fractals #cond-mat.soft #math-ph #math.DG #math.MP
paper · pdf · doi:10.1007/s10711-006-9075-y
published as Geometriae Dedicata 120 (2006) 229 · 16 pages
arxiv created 2006/01/20 · openalex publication_date 2006/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers becomes highly nontrivial. We discuss various topological and geometrical aspects of these materials and present recent progress on finding some exact layer configurations. We also exhibit connections to the study of certain embedded minimal surfaces and briefly summarize some important open problems.