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The theory of strong uniqueness polynomials, satisfying the separation condition (first introduced by Fujimoto \cite{Fuj1}), for complex meromorphic functions is quite complete. We construct examples of strong uniqueness polynomials which do not necessary satisfy the separation condition by constructing regular 1-forms of Wronskian type, a method introduced in \cite{AWW}. We also use this method to produce a much easier proof in establishing the necessary and sufficient conditions for a polynomial, satisfying the separation condition, to be a strong uniqueness polynomials for meromorphic functions and rational functions.

We study the Carath\'{e}odory and Kobayashi metrics by way of the method of dual extremal problems in functional analysis. Particularly incisive results are obtained for convex domains.

The paper is a contribution of the conjecture of Kobayashi that the complement of a generic plain curve of degree at least five is hyperbolic. The main result is that the complement of a generic configuration of three quadrics is hyperbolic and hyperbolically embedded as well as the complement of two quadrics and a line., Comment: LaTeX

The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a line and three quadrics. The main results are Let C be the union of three curves in P_2 whose degrees are at least two, one of which is at least three. Then for generic such configurations the complement of C is hyperbolic and hyperbolically embedded. The same statement holds for complements of curves in generic hypersurfaces X of degree at least five and curves which are intersections of X with hypersurfaces of degree at least five. Furthermore results are shown for curves on surfaces with picard number one., Comment: 26 pages, LaTeX