Communications in Analysis and Geometry

Volume 11 (2003)

Number 2

Closed Geodesics on Oval Surfaces and Pattern Formation

Pages: 223 – 233



C. E. Garza-Hume

P. Padilla


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.

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