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Borel theorem for CR-maps

Banff International Research Station for Mathematical Innovation and Discovery

Following Henri Poincare, numerous results in Dynamics establish the curious phenomenon saying that two smooth objects (e.g., vector fields), which can be transformed into each other by means of a formal power series transformation, can be also transformed into each other by a smooth map. This is a kind of analogue of Borel Theorem on smooth realizations of formal power series. In CR-geometry, similar phenomena hold for real-analytic CR-manifolds, and the usual outcome is that two formally equivalent CR-manifolds are also equivalent holomorphically. However, in our recent work with Shafikov we proved that there exist real-analytic CR-manifolds, which are equivalent formally, but still not holomorphically. On the other hand, in our more recent work with Lamel and Stolovitch we prove that the following is true: if two 3-dimensional real-analytic CR-manifolds are equivalent formally, then they are $C^\infty$ CR-equivalent. In this talk, I will outline the latter result.

Mathematics; Several complex variables and analytic spaces; Potential theory; Global analysis

video/mp4

Author affiliation: University of Vienna

2017-02-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59648

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/