Communications in Analysis and Geometry

Volume 11 (2003)

Number 2

Closed Geodesics on Oval Surfaces and Pattern Formation

Pages: 223 – 233

DOI: https://dx.doi.org/10.4310/CAG.2003.v11.n2.a3

Authors

C. E. Garza-Hume

P. Padilla

Abstract

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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Published 1 January 2003