On the capacity of a plane condenser and conformal mapping.
On the Distribution of Tsuji Points.
On the Green's Fundamental Domain.
On the inner parts of certain analytic functions
On the Integrability of the Derivative of a Quasiregular Mapping.
On the reduced modulus of a half-strip.
On Univalent Functions, Bloch Functions and VMOA.
On V. I Smirnov domains.
Painlevé's problem and analytic capacity.
In this paper we survey some recent results in connection with the so called Painlevé's problem and the semiadditivity of analytic capacity γ. In particular, we give the detailed proof of the semiadditivity of the capacity γ+, and we show almost completely all the arguments for the proof of the comparability between γ and γ+.
Periodic quasiregular mappings of finite order.
The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.
Polarization, conformal invariants and Brownian motion.
Quasiconformal circles and Lipschitz classes.
Radial Averaging Transformations and Generalized Capacities.
Radial growth and variation of univalent functions and of Dirichlet finite holomorphic functions
A well known result of Beurling asserts that if f is a function which is analytic in the unit disc and if either f is univalent or f has a finite Dirichlet integral then the set of points for which the radial variation is infinite is a set of logarithmic capacity zero. In this paper we prove that this result is sharp in a very strong sense. Also, we prove that if f is as above then the set of points such that as r → 1 is a set of logarithmic capacity zero. In particular, our results give...
Realizing step functions as harmonic measure distributions of planar domains.
Rectifiability, analytic capacity, and singular integrals.
Rectifiable sets and the Traveling Salesman Problem.
Removable sets for Lipschitz harmonic functions in the plane.
The main motivation for this work comes from the century-old Painlevé problem: try to characterize geometrically removable sets for bounded analytic functions in C.
Removable singularities for spaces of analytic functions, .
Représentation conforme et symétries: une détermination élémentaire du module d'un quadrilatère en forme de L.