157 research outputs found
Value distribution and potential theory
We describe some results of value distribution theory of holomorphic curves
and quasiregular maps, which are obtained using potential theory. Among the
results discussed are: extensions of Picard's theorems to quasiregular maps
between Riemannian manifolds, a version of the Second Main Theorem of
Nevanlinna for curves in projective space and non-linear divisors, description
of extremal functions in Nevanlinna theory and results related to Cartan's 1928
conjecture on holomorphic curves in the unit disc omitting hyperplanes
Elementary proof of the B. and M. Shapiro conjecture for rational functions
We give a new elementary proof of the following theorem: if all critical
points of a rational function g belong to the real line then there exists a
fractional linear transformation L such that L(g) is a real rational function.
Then we interpret the result in terms of Fuchsian differential equations whose
general solution is a polynomial and in terms of electrostatics.Comment: 21 page
On metrics of curvature 1 with four conic singularities on tori and on the sphere
We discuss conformal metrics of curvature 1 on tori and on the sphere, with
four conic singularities whose angles are multiples of pi/2. Besides some
general results we study in detail the family of such symmetric metrics on the
sphere, with angles (pi/2,3pi/2,pi/2,3pi/2).Comment: 25 pages, 5 figure
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