On the local meromorphic extension of CR meromorphic mappings

Since the works of Trépreau, Tumanov and Jöricke, extendability properties of CR functions on a smooth CR manifold M became fairly well understood. In a natural way, 1) M is seen to be a disjoint union of CR bricks, called CR orbits, each of which being an immersed CR submanifold of M with the same CR dimension as M Key words and phrases: CR generic currents, scarred CR manifolds, removable singularities for CR functions, deformations of analytic discs, CR meromorphic mappings. We would like to mention that these removability results were originally impulsed by Jöricke in The goal of this article is to push forward meromorphic extension on CR manifolds of arbitrary codimension, the analogs of domains being wedges over CR manifolds. It seems natural to use the theory of Trépreau-Tumanov in this context. Knowing thinness of Σ f (Sarkis) and using wedge removable singularities theorems ([15], Acknowledgements. We are grateful to Professor Henkin who raised the question. We also wish to address special thanks to Frederic Sarkis. He has communicated to us the reduction of meromorphic extension of CR meromorphic mappings to a removable singularity property and we had several interesting conversations with him

Application of complex analysis to second order equations of mixed type

Abstract. This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent'ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem for integral equations. In Using a conformal mapping, we may assume that Γ = {|z − 1| = 1, y ≥ 0}. We consider the second order linear equation of mixed type where A, B, C, E are functions of z (∈ D) and ε is a real parameter. Its complex form is the following equation of second order: 1991 Mathematics Subject Classification: Primary 35M10. Key words and phrases: discontinuous Poincaré problem, equations of mixed type, complex analytic method. [221