Existence of curves with constant geodesic curvature in a Riemannian 2-sphere

Abstract

We prove the existence of immersed closed curves of constant geodesic curvature in an arbitrary Riemannian 2-sphere for almost every prescribed curvature. To achieve this, we develop a min-max scheme for a weighted length functional.

20 pages. To appear in Transactions of the American Mathematical Society

References in corpus (1)

• The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere