Planar closed curves with prescribed curvature
Paolo Caldiroli, Anna Capietto

TL;DR
This paper proves the existence of planar closed curves with specific curvature functions using variational methods and a novel approach to ensure bounded sequences.
Contribution
It introduces a new variational approach combined with a parameter and the monotonicity trick to establish existence results for prescribed curvature curves.
Findings
Existence of closed curves with prescribed curvature for certain functions
Application of the monotonicity trick to geometric variational problems
Development of a method to obtain bounded Palais-Smale sequences
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
