Work

Weak elastic energy of rectifiable curves in the sphere

Year: 2026

Type: article

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 W2,p.

Source: Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

DOI: 10.1098/rspa.2025.0782

Authors: Domenico Mucci, Alberto Saracco, Cristian Sopio

Institutions: University of Parma, University of Ferrara

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W7154403887

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Cites: 11

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