 068 Isabeau Birindelli, Enrico Valdinoci
 The GinzburgLandau equation
in the Heisenberg group
(114K, LATeX)
Jan 11, 06

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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,
planelike 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.
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