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

[BibTeX]

preprint

Inserted: 10 jan 2023

Year: 2023

ArXiv: 2301.03525 PDF

Abstract:

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.