A Cantor regular set which does not have Markov's property
A new setting for potential theory. I
We consider a transient Hunt process in which the potential density satisfies the conditions: (a) for each , is finite continuous in ; (b) iff . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).
A note on the local structure of levels of a plane vector field
A remark on polygonal quasiconformal maps.
A symmetrization inequality for plurisubharmonic functions.
A Unified Theory of Harmonic Measures and Capacitary Potentials.
An estimate from below for the Markov constant of a Cantor repeller
An extremal problem for certain subharmonic functions in the plane.
An extremal problem for harmonic measure.
Analytic approach to semiclassical logarithmic potential theory
Analytic capacity and linear measure
Beiträge zum potentialtheoretischen Aspekt des Verheftungssatzes von A.D. Alexandrow.
Boundary limits of Green's potentials along curves
Bounds for capacities in terms of asymmetry.
Caloric measure on domains bounded by Weierstrass-type graphs.
Capacité analytique et le problème de Painlevé
Le problème de Painlevé consiste à trouver une caractérisation géométrique des sous-ensembles du plan complexe qui sont effaçables pour les fonctions holomorphes bornées. Ce problème d’analyse complexe a connu ces dernières années des avancées étonnantes, essentiellement grâce au dévelopement de techniques fines d’analyse réelle et de théorie de la mesure géométrique. Dans cet exposé, nous allons présenter et discuter une solution proposée par X. Tolsa en termes de courbure de Menger au problème...
Computing logarithmic capacity with linear programming.
Correction of some misprints in my paper “Potentials and boundary value problems” published in “Wissenschaftliche Schriftenreihe der T. H. Karl-Marx-Stadt”
Covering Theorems for Univalent Functions.
Dimension of the harmonic measure of non-homogeneous Cantor sets
We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets is a continuous function of the parameters determining these sets. This results extends a previous one of the author and do not use ergotic theoretic tools, not applicables to our case.