OSU Mathematics Seminars and Colloquia
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Mon, Feb 17, 2020
Analysis Seminar
2:30 PM
MSCS 509
Severi's theorem for CR singular submanifolds of codimension two
Jiri Lebl, Oklahoma State University
Host: Octavian Mitrea
[Abstract] [PDF]
Abstract: It is well-known that a real-analytic function on the real line is a restriction of a holomorphic (analytic) function. In several complex variables there are more kinds of submanifolds than just real curves. Severi's theorem says that a real-analytic CR function on a real-analytic CR submanifold is a restriction of a holomorphic function. So the Cauchy-Riemann equations restricted to the manifold are enough. We extend this result to some CR singular submanifolds, that is when the Cauchy-Riemann equations induce a problem with a characteristic point. It is joint work with Alan Noell and Sivaguru Ravisankar.
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