Motion of an elastic wire with thickness in a Riemannian manifold

Abstract: There are several types of equation of motion of elastic wires. In this paper, we treat an equation taking account of the thickness of wire. The equation was introduced by Caflisch and Maddocks on plane curves, and they proved the existence of solutions. Koiso and Sugimoto generalized the result to any dimensional Euclidean space. In this paper, we will prove the existence of solutions on any riemannian manifold.