Analysis and Mathematical Physics

• From Diff (S 1) to Univalent Functions. Cases of Degeneracy.- Poincaré—Steklov Integral Equations and Moduli of Pants.- Generalized Hamilton—Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups.- Bergen Lecture on -Neumann Problem.- Numerical Scheme for Laplacian Growth Models Based on the Helmholtz—Kirchhoff Method.- Gravitational Lensing by Elliptical Galaxies, and the Schwarz Function.- Nevanlinna Domains in Problems of Polyanalytic Polynomial Approximation.- Potential Theory in Denjoy Domains.- Carathéodory Convergence of Immediate Basins of Attraction to a Siegel Disk.- Rings and Lipschitz Continuity of Quasiconformal Mappings.- A Theoretical Algorithm to get a Schottky Uniformization from a Fuchsian one.- Scattering from Sparse Potentials: a Deterministic Approach.- Application of ATS in a Quantum-optical Model.- Geometry of Carnot-Carathéodory Spaces, Differentiability, Coarea and Area Formulas.- Fourier Transforms of UD Integrals.- Fredholm Eigenvalues of Jordan Curves: Geometric, Variational and Computational Aspects.- A Note on Life-span of Classical Solutions to the Hele—Shaw Problem.- The Fourier Transforms of General Monotone Functions.- Traces of Hörmander Algebras on Discrete Sequences.- Resonance Dynamics and Decoherence.- Ramified Integrals, Casselman Phenomenon, and Holomorphic Continuations of Group Representations.- The Stability of Solitary Waves of Depression.- Singular and Tangent Slit Solutions to the Löwner Equation.- A Remark on Amoebas in Higher Codimensions.- Quadratic Differentials and Weighted Graphs on Compact Surfaces.- Riesz Transforms and Rectifiability.

From the reviews:“This volume is based on lectures delivered at the International Conference ‘New trends in Harmonic and Complex Analysis’, held May 7-12, 2007 … . results presented in this volume trace further developments of frontier research exploring the bridge between complex real analysis potential theory partial differential equations and modern topics of fluid mechanics and mathematical physics. The present volume will be of interest for specialists and graduate students in mathematics and mathematical physics. Many papers in this volume are surveys whereas others represent original research.” (L'Enseignement Mathématique, Vol. 56 (2), 2010)