- 00-368 L.A. Caffarelli, R. de la Llave
- Plane-like minimizers in periodic media
Sep 18, 00
(auto. generated pdf),
of related papers
Abstract. We show that given an elliptic integrand $\J$ in
$\real^d$ which is periodic under integer
translations, given any plane in $\real^d$, there is
at least one minimizer of $\J$
which remains at a bounded distance from this
plane. This distance can be bounded uniformly
on the planes.
We also show that, when folded back
to $\real^d/\integer^d$ the minimizers
we construct give rise to a lamination.
One particular case of these
results is minimal surfaces for metrics
invariant under integer translations.
The same results hold for
other functionals that
involve volume terms (small and average zero).
In such a case the minimizers satisfy the prescribed mean curvature
equation. A further generalization allows to formulate
and prove similar results in other manifolds than the torus
provided that their fundamental group and universal cover satify