English

On the uniqueness of energy-minimizing curves in constrained spaces

Differential Geometry 2023-07-21 v2

Abstract

In this paper, we investigate energy-minimizing curves with fixed endpoints pp and qq in a constrained space. We prove that when one of the endpoints, say pp, is fixed, the set of points qq for which the energy-minimizing curve is not unique has no interior points.

Keywords

Cite

@article{arxiv.2306.07511,
  title  = {On the uniqueness of energy-minimizing curves in constrained spaces},
  author = {Ki-Ahm Lee and Taehun Lee},
  journal= {arXiv preprint arXiv:2306.07511},
  year   = {2023}
}