2024/05/25 by André M. Sonnet, Sonnet, André M., Epifanio G. Virga +1 · 4 citations
Engineering · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Composite Structure Analysis and Optimization #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2405.16169
openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we identify a bending content and a class of deformations that leave it unchanged. These are the bending-neutral deformations, fully characterized by an integrability condition; they preserve normals. We prove that (1) every minimal surface is transformed into a minimal surface by a bending-neutral deformation, (2) given two minimal surfaces with the same system of normals, there is a bending-neutral deformation that maps one into the other, and (3) all minimal surfaces have indeed a universal bending content.