De Rham cohomology of manifolds containing the points of infinite type, and Sobolev estimates for the $$\bar partial - Neumann$$ problem Academic Article uri icon

abstract

  • We consider smooth bounded pseudoconvex domains in Cn whose boundary points of infinite type are contained in a smooth submanifold M (with or without boundary) of the boundary having its (real) tangent space at each point contained in the null space of the Levi form of b at the point. (In particular, complex submanifolds satisfy this condition.) We consider a certain one-form on b and show that it represents a De Rham cohomology class on submanifolds of the kind described. We prove that if represents the trivial cohomology class on M, then the Bergman projection and the {Mathematical expression} operator on are continuous in Sobolev norms. This happens, in particular, if M has trivial first De Rham cohomology, for instance, if M is simply connected. 1993 Mathematica Josephina, Inc.

published proceedings

  • Journal of Geometric Analysis

author list (cited authors)

  • Boas, H. P., & Straube, E. J.

citation count

  • 22

complete list of authors

  • Boas, Harold P||Straube, Emil J

publication date

  • May 1993