9 papers · 1 filter
Weak pseudoconcavity and the maximum modulus principle
C. Denson Hill, Mauro Nacinovich
We discuss the maximum modulus principle, and weak unique continuation, for CR functions on an abstract almost CR manifold M. We investigate these matters under the assumption of w…
Obstructions to generic embeddings
Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich
In Grauert's paper [G] it is noted that finite dimensionality of cohomology groups sometimes implies vanishing of these cohomomogy groups. Later on Laufer formulated a zero or infi…
The Poincare lemma and local embeddability
Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich
For pseudoconvex abstract CR manifolds, the validity of the Poincare Lemma for (0,1) forms implies local embeddability in C^N. The two properties are equivalent for hypersurfaces o…
Remarks on weakly pseudoconvex boundaries
Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich
In this paper, we consider the boundary M of a weakly pseudoconvex domain in a Stein manifold. We point out a striking difference between the local cohomology and the global cohomo…
Remarks on weakly pseudoconvex boundaries: Erratum
Judith Brinkschulte, C. Denson Hill, Mauro Nacinovich
We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
Stein fillability and the realization of contact manifolds
C. Denson Hill, Mauro Nacinovich
There is an intrinsic notion of what it means for a contact manifold to be the smooth boundary of a Stein manifold. The same concept has another more extrinsic formulation, which i…