Ilya Kossovskiy: On the analyticity of CR-diffeomorphisms
Title: On the analyticity of CR-diffeomorphisms.
Abstract: One of the fundamental objects in Several Complex Variables are CR-mappings. CR-mappings naturally occur in Complex Analysis as boundary values of mappings between domains, and as restrictions of holomorphic mappings onto real submanifolds. It was already observed by Cartan that smooth CR-diffeomorphisms between CR-submanifolds in C^N tend to be very regular, i.e. they are restrictions of holomorphic maps. However, in general smooth CR-mappings form a more restictive class of mappings. Thus, since the inception of CR-geometry, the following general question is of fundamental importance for the field: Are CR-equivalent real-analytic CR-structures also equivalent holomorphically? In our joint work with B. Lamel, we answer this question in the negative way, in any positive CR-dimension and CR-codimension. Our construction is based on a recent Dynamical technique in CR-geometry, developed in my earlier work with Shafikov.
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