Speaker: Prof. Mei-chi Shaw (University of Notre Dame)
Title: The Cauchy-Riemann equations in complex projective spaces
Time: 2007-08-23 (Thu.)  15:00 -
Abstract:  In this talk we discuss the Cauchy-Riemann equations in complex projective spaces. We use bounded plurisubharmonic exhaustion functions on pseudoconvex domains to study the $\bar\partial$ problem with weights in complex projective spaces. Global regularity for the Cauchy-Riemann equations on both pseudoconvex and pseudoconcave domains up to the boundary will be analyzed. The solutions are used to study the function theory via the $\bar\partial$-Cauchy problem. We also discuss the application to the nonexistence of Lipschitz Levi-flat hypersurfaces in the complex projective space of dimension at least three, which removes the smoothness requirement used in an earlier paper of Siu (Joint work with Jianguo Cao).
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