Isabeau Birindelli, Enrico Valdinoci
The Ginzburg-Landau equation
in the Heisenberg group
(114K, LATeX)
ABSTRACT. We consider
a functional related with
phase transition models in
the Heisenberg group
framework. We prove that
level sets of local minimizers
satisfy some density estimates,
that is, they behave as ``codimension one" sets.
We thus deduce a uniform
convergence property of these level sets
to interfaces with minimal area.
These results are then applied in the construction
of (qua\-si)periodic,
plane-like minimizers, i.e., minimizers of our functional
whose level sets are contained in a spacial slab of
universal size in a prescribed direction.
As a limiting case, we obtain the existence of
hypersurfaces contained in such a slab which minimize
the surface area with respect to a given periodic metric.