Journal article
Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces in
Mathematische Zeitschrift, Vol.248(1), pp.183-221
09/2004
DOI: 10.1007/s00209-004-0661-0
Abstract
Let Ω be a pseudoconvex domain with C2 boundary in , n ≥ 2. We prove that the -Neumann operator N exists for square-integrable forms on Ω. Furthermore, there exists a number ε0>0 such that the operators and the Bergman projection are regular in the Sobolev space Wε ( Ω) for ε<ε0. The -Neumann operator is used to construct -closed extension on Ω for forms on the boundary bΩ. This gives solvability for the tangential Cauchy-Riemann operators on the boundary. Using these results, we show that there exist no non-zero L2-holomorphic (p, 0)-forms on any domain with C2 pseudoconcave boundary in with p > 0 and n ≥ 2. As a consequence, we prove the nonexistence of C2 Levi-flat hypersurfaces in .
Details
- Title: Subtitle
- Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces in
- Creators
- Jianguo Cao - Department of Mathematics University of Notre Dame Notre DameIN 46556USAMei-Chi Shaw - Department of Mathematics University of Notre Dame Notre DameIN 46556USALihe Wang - Department of Mathematics University of Iowa Iowa CityIA 52242USA
- Resource Type
- Journal article
- Publication Details
- Mathematische Zeitschrift, Vol.248(1), pp.183-221
- Publisher
- Springer-Verlag
- DOI
- 10.1007/s00209-004-0661-0
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- Language
- English
- Date published
- 09/2004
- Academic Unit
- Mathematics
- Record Identifier
- 9984083249502771
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