Deformations of Mathematical Structures: Complex Analysis with Physical Applications

I. Proceedings of the Third Finnish-Polish Summer School in Complex Analysis.- (Quasi) Conformal Deformation.- Some elliptic operators in real and complex analysis.- Embedding of Sobolev spaces into Lipschitz spaces.- Quasiregular mappings from ?n to closed orientable n-manifolds.- Some upper bounds for the spherical derivative.- On the connection between the Nevanlinna characteristics of an entire function and of its derivative.- Foliations.- Characteristic homomorphism for transversely holomorphic foliations via the Cauchy-Riemann equations.- Complex premanifolds and foliations.- Geometric Algebra.- Mo?bius transformations and Clifford algebras of euclidean and anti-euclidean spaces.- II. Complex Analytic Geometry.- Uniformization.- Doubles of atoroidal manifolds, their conformal uniformization and deformations.- Hyperbolic Riemann surfaces with the trivial group of automorphisms.- Algebraic Geometry.- On the Hilbert scheme of curves in a smooth quadric.- A contribution to Keller’s Jacobian conjecture II.- Local properties of intersection multiplicity.- Generalized Padé approximants of Kakehashi’s type and meromorphic continuation of functions.- Several Complex Variables.- Three remarks about the Caratheodory distance.- On the convexity of the Kobayashi indicatrix.- Boundary regularity of the solution of the ??-equation in the polydisc.- Holomorphic chains and extendability of holomorphic mappings.- Remarks on the versal families of deformations of holomorphic and transversely holomorphic foliations.- Hurwitz Pairs.- Hurwitz pairs and octonions.- Hermitian pre-Hurwitz pairs and the Minkowski space.- III. Real Analytic Geometry.- (Quasi) Conformal Deformation.- Morphisms of Klein surfaces and Stoilow’s topological theory of analytic functions.- Generalizedgradients and asymptotics of the functional trace.- Holomorphic quasiconformal mappings in infinite-dimensional spaces.- Algebraic Geometry.- Product singularities and quotients of linear groups.- Approximation and extension of C? functions defined on compact subsets of ?n.- Potential Theory.- New existence theorems and evaluation formulas for analytic Feynman integrals.- On the construction of potential vectors and generalized potential vectors depending on time by a contraction principle.- Symbolic calculus applied to convex functions and associated diffusions.- Lagrangian for the so-called non-potential system: the case of magnetic monopoles.- Hermitian Geometry.- Examples of deformations of almost hermitian structures.