Geometric sufficient conditions for compactness of the complex Green operator

2010/10/18 by Samangi Munasinghe, Munasinghe, Samangi, Emil J. Straube +1
Mathematics · #32V99 #32W10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32V99 #msc:32W10

paper · pdf · doi:10.48550/arxiv.1010.3665

19 pages

arxiv created 2010/10/25 · arxiv updated 2010/10/26

Abstract

We establish compactness estimates for ∂_M on a compact pseudoconvex CR-submanifold M of ℂⁿ of hypersurface type that satisfies the (analogue of the) geometric sufficient conditions for compactness of the ∂-Neumann operator given by the authors earlier. These conditions are formulated in terms of certain short time flows in complex tangential directions.

Related

• The complex Green operator on CR-submanifolds of ℂⁿ of hypersurface type: compactness
• Complex tangential flows and compactness of the ∂- Neumann operator
• Geometric conditions which imply compactness of the ∂-Neumann operator
• Estimates for the complex Green operator: symmetry, percolation, and\n interpolation
• Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type