Tohoku Mathematical Journal
2002
June
SECOND SERIES VOL. 54, NO. 2

Tohoku Math. J.
54 (2002), 179-193

Title KIRCHHOFF ELASTIC RODS IN A RIEMANNIAN MANIFOLD

Author Satoshi Kawakubo

(Received May 10, 2000, revised January 22, 2001)
Abstract. Imagine a thin elastic rod like a piano wire. We consider the situation that the elastic rod is bent and twisted and both ends are welded together to form a smooth loop. Then, does there exist a stable equilibrium? In this paper, we generalize the energy of uniform symmetric Kirchhoff elastic rods in the 3-dimensional Euclidean space to consider such a variational problem in a Riemannian manifold. We give the existence and regularity of minimizers of the energy in a compact or homogeneous Riemannian manifold.

2000 Mathematics Subject Classification. Primary 58E10; Secondary 74K10.

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