Contents Online
Mathematical Research Letters
Volume 30 (2023)
Number 4
Whitney–Graustein homotopy of locally convex curves via a curvature flow
Pages: 1045 – 1062
DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n4.a3
Author
Abstract
Let $X_0, \tilde{X}$ be two smooth, closed and locally convex curves in the plane with same winding number. A curvature flow with a nonlocal term is constructed to evolve $X_0$ into $\tilde{X}$. It is proved that this flow exits globally, preserves both the local convexity and the elastic energy of the evolving curve. If the two curves have same elastic energy then the curvature flow deforms the evolving curve into the target curve $\tilde{X}$ as time tends to infinity.
Received 17 September 2020
Accepted 6 September 2022
Published 3 April 2024