Boundary regularity and the uniform convergence of quasiconformal mappings.
Boundary subordination
We study the idea of the boundary subordination of two analytic functions. Some basic properties of the boundary subordination are discussed. Applications to classes of univalent functions referring to a boundary point are demonstrated.
Boundary value problems for analytic and harmonic functions in domains with nonsmooth boundaries. Applications to conformal mappings.
Boundary values and the transformation problem for constant principal strain mappings.
Bounded functions starlike with respect to symmetrical points.
Bounded functions with positive real part
Bounded holomorphic functions with multiple sheeted pluripolar hulls
We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.
Bounded Montel univalent functions
Bounded spiral-like functions with fixed second coefficient.
Bounded Turning and Quasiconformal Maps.
Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions
It is known that if is holomorphic in the open unit disc of the complex plane and if, for some , , , then . We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in . In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.
Bounds of the roots of the real polynomial
An algorithm for the calculation of a lower bound of the absolute values of the roots of a real algebraic polynomial, of an arbitrary degree, is derived. An example is given to compare the bounds calculated by the method proposed and by other methods.
Bounds on the curvature for functions with bounded boundary rotation of order 1-b.
Braiding of the attractor and the failure of iterative algorithms.
Canonical mappings in
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...
Capacity relations in a flat quadrilateral.
Capacity theory on algebraic curves and canonical heights
Capacity theory on varieties
Carleson measure and monogenic functions
We present necessary and sufficient conditions for a measure to be a p-Carleson measure, based on the Poisson and Poisson-Szegő kernels of the n-dimensional unit ball.