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Mei-Chi Shaw

2008-03-11
14:00:00 - 15:00:00

The Strong Oka’s Lemma, bounded plurisubharmonic functions and the -Neumann problem

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk we discuss the Cauchy-Riemann equations on pseudoconvex domains with Lipschitz domains in complex manifolds. A unified approach to the regularity of the -Neumann problem for Lipschitz domains will be given using the strong Oka’s lemma. We will also discuss the relationship between the strong Oka’s lemma,bounded plurisubharmonic exhaustion functions and their relationship with the regularity of the -Neumann problem in complex projective spaces. Applications to the nonexistence of Levi-flat hypersurfaces in complex projective spaces will be discussed.