Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature

2014/03/13 by Julià Cufí, Cufí, Julià, Agustí Reventós +1
Mathematics · Physics and Astronomy · #53A04 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53A04

paper · pdf · doi:10.48550/arxiv.1403.3236

16 pages, 3 figures

arxiv created 2014/03/13 · openalex publication_date 2014/03/13 · arxiv updated 2014/03/14 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

We relate the total curvature and the isoperimetric deficit of a curve γ in a two-dimensional space of constant curvature with the area enclosed by the evolute of γ. We provide also a Gauss-Bonnet theorem for a special class of evolutes.

Related

• Buffon's Problem determines Gaussian Curvature in three Geometries
• Isoperimetric problems and lower bounds on curvature
• Some results on evolutoids of convex curves in 2-dimensional space forms
• A discrete Gauss-Bonnet type theorem
• Isoperimetric Regions in Nonpositively Curved Manifolds