2014/11/22 by Vincenzo Ferone, Ferone, Vincenzo, Bernd Kawohl +3 · 1 citation
Computer Science · Mathematics · #49Q19 #51M16 #53C44 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC) #Point processes and geometric inequalities
paper · doi:10.48550/arxiv.1411.6100
openalex publication_date 2014/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the elastic energy E(γ) of a closed curve γ has a minimizer among all plane simple regular closed curves of given enclosed area A(γ), and that the minimum is attained for a circle. The proof is of a geometric nature and deforms parts of γ in a finite number of steps to construct some related convex sets with smaller energy.