These Proceedings contain selected papers by the speakers invited to the Seminar on Deformations, organized in 1985/87 by Julian tawryno- wicz (t6dz), whose most fruitful parts took place in 1986 in Lublin during the 3rd Finnish-Polish Summer School in Complex Analysis [in cooperation with O. Martio (JyvliskyHl)] held simultaneously with the 9th Conference on Analytic Function in Poland [in cooperation with S. Dimiev (Sofia), P. Dolbeault (Paris), K. Spallek (Bochum), and E. Vesen- tini (Pisa)]. The Lublin session of the Seminar, organized jointly with S. Dimiev and K. Spallek, was preceded by a session organized by them at Druzhba (near Varna) in 1985 and followed by a similar session at Druzhba in 1987. The collection contains 31 papers connected with deformations of mathematical structures in the context of complex analysis with physi- cal applications: (quasi)conformal deformation uniformization, potential theory, several complex variables, geometric algebra, algebraic ge- ometry, foliations, Hurwitz pairs, and Hermitian geometry. They are research papers in final form: no version of them will be submitted for publication elsewhere.
In contrast to the previous volume (Seminar on Deformations, Proceedings, L6dz-WarsaUJ 1982/84, ed. by J. -i:.awrynowicz, Lecture Notes in Math. 1165, Springer, Berlin-Heidelberg- -New York-Tokyo 1985, X + 331 pp.) open problems are not published as separate research notes, but are included in the papers.
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 Pade 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.- Generalized gradients 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.