Stability problem of equilibrium discrete planar curves
Differential Geometry
2020-04-17 v1
Abstract
In this paper, we study planar polygonal curves from the variational methods. We show an unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first variation of the length functional. Moreover, we determine the equilibrium curves for the length functional under the area-constraint condition and study their stability.
Cite
@article{arxiv.2004.07475,
title = {Stability problem of equilibrium discrete planar curves},
author = {Yoshiki Jikumaru},
journal= {arXiv preprint arXiv:2004.07475},
year = {2020}
}
Comments
20 pages, 8 figures