Real-analytic coordinates for smooth strictly pseudoconvex CR-structures

2019/06/24 by Ilya Kossovskiy, Kossovskiy, Ilya, Dmitri Zaitsev +1 · 2 citations
Mathematics · #Holomorphic and Operator Theory #Mathematics and Applications #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1906.09989

Abstract

For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the canonically associated function expressing 2-jets of the formal Segre varieties in terms of their 1-jets. We also express this condition in equivalent terms for a Fefferman type determinant

Cited by

• Strong Ramadanov Conjecture for Real Ellipsoids in \mathbb C²: two approaches
• Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I

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