學術演講
主講者: | Prof. Mei-chi Shaw (University of Notre Dame) |
講題: | The Cauchy-Riemann equations in complex projective spaces |
時間: | 2007-08-23 (Thu.) 15:00 - |
地點: | |
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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