Closed Geodesics on Oval Surfaces and Pattern Formation
C. E. Garza-Hume, Pablo Padilla · Communications in Analysis and Geometry · 2003
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.