Planar closed curves with prescribed curvature

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.

13 pages

References in corpus (4)

• An Obstruction to the Existence of Immersed Curves of Prescribed Curvature
• On the dynamics of a charged particle in magnetic fields with cylindrical symmetry
• Finite-time singularity formation for the heat flow of the $H$-system
• Planar loops with prescribed curvature via Hardy's inequality