Planar closed curves with prescribed curvature

Published 1 Jul 2024 in math.DG | (2407.01062v1)

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.

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