The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Table of Contents:
Stable expansions in homogeneous polynomials by L. Aizenberg and N. Tarkhanov Dynamics of approximate solutions to a class of evolution equations in Banach spaces by S. Aizicovici, S. Reich, and A. J. Zaslavski Schottky's theorem on conformal mappings between annuli: A play of derivatives and integrals by K. Astala, T. Iwaniec, G. Martin, and J. Onninen Univalent convex functions in the positive direction of the real axis by D. Bshouty and A. Lyzzaik The common fixed point set of commuting nonexpansive mappings in infinite products of unit balls by M. Budzynska and T. Kuczumow Controlled approximation for some classes of holomorphic functions by M. Elin, D. Shoikhet, and L. Zalcman Best approximating entire functions to $\left\vert x\right\vert ^{\alpha}$ in $L_2$ by M. I. Ganzburg and D. S. Lubinsky Orbits of tori extended by finite groups and their polynomial hulls: The case of connected complex orbits by V. M. Gichev QC Riemann mapping theorem in space by D. H. Hamilton Boundary value problems in weighted edge spaces by G. Harutyunyan and B.-W. Schulze Analytic properties of Besov spaces via Bergman projections by H. T. Kaptanoglu and A. E. Ureyen The Cauchy integral over non-rectifiable paths by B. A. Kats Holomorphic continuation via Laplace-Fourier series by O. Kounchev and H. Render Analytic functions in algebras by Y. Krasnov Rational approximation of holomorphic functions and geometry of Grunsky inequalities by S. L. Krushkal Quadratic forms in geometric function theory, quasiconformal extensions, Fredholm eigenvalues by R. Kuhnau Elimination methods of unknowns from nonlinear systems by A. Kytmanov On locally biholomorphic finitely valent mappings from multiply connected to simply connected domains by P. Liczberski and V. V. Starkov Parabolic pseudodifferential operators in exponential weighted spaces by Y. Lutsky and V. S. Rabinovich The Cauchy problem of couple-stress elasticity by O. Makhmudov, I. Niyozov, and N. Tarkhanov On the zeta-function of a nonlinear system by S. Myslivets Some questions of uniqueness for extremal quasiconformal mappings by E. Reich Remarks on the existence of quasimeromorphic mappings by E. Saucan On the Cauchy problem for the Cauchy-Riemann operator in Sobolev spaces by A. Shlapunov On spectral functions for commutative $J$-self-adjoint operator families of the $D_{\kappa}^+$-class by V. Strauss Mappings associated with weighted Sobolev spaces by A. Ukhlov and S. K. Vodopyanov Inner maps and Banach algebras by E. Vesentini Reconstructing holomorphic functions in a domain from their values on a part of its boundary by A. Vidras A note on the parabolicity of minimal graphs by A. Weitsman Localization of fixed points and zeros for holomorphic maps in locally convex spaces and nonexpansive maps in J*-algebras by K. Wlodarczyk, D. Klim, and R. Kowalczyk On harmonic polynomial interpolation by V. Zahariuta.