English

Planar closed curves with prescribed curvature

Differential Geometry 2024-07-02 v1

Abstract

By variational methods, we prove existence of planar closed curves with prescribed curvature for some classes of curvature functions. The main difficulty is to obtain bounded Palais-Smale sequences. This is achieved by adding a parameter in the problem and using a version of the "monotonicity trick" introduced by M. Struwe in 1988.

Keywords

Cite

@article{arxiv.2407.01062,
  title  = {Planar closed curves with prescribed curvature},
  author = {Paolo Caldiroli and Anna Capietto},
  journal= {arXiv preprint arXiv:2407.01062},
  year   = {2024}
}

Comments

13 pages

R2 v1 2026-06-28T17:24:36.305Z