32 research outputs found
Weighted integral formulas on manifolds
We present a method of finding weighted Koppelman formulas for -forms
on -dimensional complex manifolds which admit a vector bundle of rank
over , such that the diagonal of has a defining
section. We apply the method to \Pn and find weighted Koppelman formulas for
-forms with values in a line bundle over \Pn. As an application, we
look at the cohomology groups of -forms over \Pn with values in
various line bundles, and find explicit solutions to the \dbar-equation in
some of the trivial groups. We also look at cohomology groups of -forms
over \Pn \times \Pm with values in various line bundles. Finally, we apply
our method to developing weighted Koppelman formulas on Stein manifolds.Comment: 25 page
Uniform algebras and approximation on manifolds
Let be a bounded domain and let be a uniform algebra generated by a set
of holomorphic and pluriharmonic functions. Under natural assumptions on
and we show that the only obstruction to is that there is a holomorphic disk such that all functions in are holomorphic on , i.e., the
only obstruction is the obvious one. This generalizes work by A. Izzo. We also
have a generalization of Wermer's maximality theorem to the (distinguished
boundary of the) bidisk
The Oka
Abstract:
Grauert principll without induetion over the base dimension // Math. Ann., 1998, 311