Weak elastic energy of rectifiable curves in the sphere

2025/09/11 by Mucci, Domenico, Saracco, Alberto, Sopio, Cristian
#49J45 #53A04 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.09405

Abstract

We introduce for any exponent p>1 the p-curvature functional for rectifiable curves in the two-dimensional sphere. We prove that this functional is finite and agrees with the integral of the geodesic curvature raised to the power p on curves whose arc length parameterization is in the Sobolev class W^2,p.

Citations

• Weak elastic energy of irregular curves
• Curves of Finite Total Curvature

Related

• Weak elastic energy of rectifiable curves in Riemannian surfaces
• Weak elastic energy of irregular curves
• Generalized elastica problems under area constraint
• Instability of Closed p-Elastic Curves in \mathbbS²
• Regularity and structure of non-planar p-elasticae