Estimates for the ∂̄-neumann Problem and Nonexistence of Levi-flat Hypersurfaces in Cp
نویسندگان
چکیده
Let Ω be a pseudoconvex domain with C-smooth boundary in CP. We prove that the ∂̄-Neumann operator N exists for (p, q)-forms on Ω. Furthermore, there exists a t0 > 0 such that the operators N , ∂̄N , ∂̄N and the Bergman projection are regular in the Sobolev space W (Ω̄) for t < t0. The boundary estimates above have applications in complex geometry. We use the estimates to prove the nonexistence of C real Levi-flat hypersurfaces in CP. We also show that there exist no non-zero L-holomorphic (p, 0)-forms on any pseudoconcave domain in CP with p > 0.
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