9 papers · 1 filter
Critical structures of inner functions II
Oleg Ivrii
We study the correspondence proposed in \cite{critical-structures} between inner functions modulo post-compositions with automorphisms of the unit disk and cyclic subspaces of the…
Analytic mappings of the unit disk with bounded compression
Oleg Ivrii, Artur Nicolau
In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give se…
Analytic mappings of the unit disk which almost preserve hyperbolic area
Oleg Ivrii, Artur Nicolau
In this paper, we study analytic self-maps of the unit disk which distort hyperbolic area of large hyperbolic disks by a bounded amount. We give a number of characterizations invol…
Shapes of infinite conformally balanced trees
Oleg Ivrii, Peter Lin, Steffen Rohde +1
Numerical experiments by Werness, Lee and the third author suggested that dessin d'enfants associated to large trivalent trees approximate the developed deltoid introduced by Lee,…
Critical structures of inner functions
Oleg Ivrii
A celebrated theorem of M. Heins says that up to post-composition with a Möbius transformation, a finite Blaschke product is uniquely determined by its critical points. K. Dyakonov…
Homogenization of random quasiconformal mappings and random Delauney triangulations
Oleg Ivrii, Vladimir Markovic
In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle pac…