Communications in Analysis and Geometry
Volume 11 (2003)
Closed Geodesics on Oval Surfaces and Pattern Formation
Pages: 223 – 233
We study a singularly perturbed semilinear elliptic partial differential equation with a bistable potential on an oval surface. We show that the transition region of minimizers of the associated functional with a suitable constraint converges in the sense of varifolds to a minimal closed geodesic on the surface.