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.
Inhaltsverzeichnis
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.
