1,318 research outputs found
Extremal maps of the universal hyperbolic solenoid
We show that the set of points in the Teichmuller space of the universal
hyperbolic solenoid which do not have a Teichmuller extremal representative is
generic (that is, its complement is the set of the first kind in the sense of
Baire). This is in sharp contrast with the Teichmuller space of a Riemann
surface where at least an open, dense subset has Teichmuller extremal
representatives. In addition, we provide a sufficient criteria for the
existence of Teichmuller extremal representatives in the given homotopy class.
These results indicate that there is an interesting theory of extremal (and
uniquely extremal) quasiconformal mappings on hyperbolic solenoids.Comment: LaTeX, 15 page
Ample Vector Bundles and Branched Coverings, II
In continuation of our work in Comm. in Algebra, vol. 28 (2000), we study
ramified coverings of projective manifolds, in particular over Fano manifolds
and investigate positivity properties of the associated vector bundle. Moreover
we study the topology of low degree coverings and the structure of the
ramification divisor.Comment: LaTeX, 21 page
A (2+1)-dimensional growth process with explicit stationary measures
We introduce a class of (2+1)-dimensional stochastic growth processes, that
can be seen as irreversible random dynamics of discrete interfaces.
"Irreversible" means that the interface has an average non-zero drift.
Interface configurations correspond to height functions of dimer coverings of
the infinite hexagonal or square lattice. The model can also be viewed as an
interacting driven particle system and in the totally asymmetric case the
dynamics corresponds to an infinite collection of mutually interacting
Hammersley processes.
When the dynamical asymmetry parameter equals zero, the
infinite-volume Gibbs measures (with given slope ) are
stationary and reversible. When , are not reversible any
more but, remarkably, they are still stationary. In such stationary states, we
find that the average height function at any given point grows linearly
with time with a non-zero speed: while the typical fluctuations of are
smaller than any power of as .
In the totally asymmetric case of and on the hexagonal lattice, the
dynamics coincides with the "anisotropic KPZ growth model" introduced by A.
Borodin and P. L. Ferrari. For a suitably chosen, "integrable", initial
condition (that is very far from the stationary state), they were able to
determine the hydrodynamic limit and a CLT for interface fluctuations on scale
, exploiting the fact that in that case certain space-time
height correlations can be computed exactly.Comment: 37 pages, 13 figures. v3: some references added, introduction
expanded, minor changes in the bul
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