Calculus of Variations and Geometric Measure Theory

G. Bevilacqua - L. Lussardi - A. Marzocchi

Geometric invariants of non-smooth framed curves

created by bevilacqua on 10 Jan 2023
modified by lussardi on 23 Jan 2024


Accepted Paper

Inserted: 10 jan 2023
Last Updated: 23 jan 2024

Journal: INdAM Springer Series
Year: 2023

ArXiv: 2301.03525 PDF


We compare the Serret-Frenet frame with a {\em relatively parallel adapted frame} (RPAF) introduced by Bishop to parametrize $W^{2,2}$-curves. Next, we derive the geometric invariants, curvature and torsion, with the RPAF associated to the curve. Finally, we discuss applications of the two approaches in variational problems.