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TITLE Pseudoconvex domains with smooth boundary in projective spaces
KIAS AUTHORS Sibony, Nessim
JOURNAL MATHEMATISCHE ZEITSCHRIFT, 2021
ARCHIVE  
ABSTRACT Given a pseudoconvex domain U with C-1-boundary in P-n, n >= 3, we show that if H-dR(2n-2) (U)not equal 0, then there is a strictly psh function in a neighborhood of partial derivative U. We also solve the partial derivative-equation in X = P-n \ U, for data in C-(0,1)(infinity) (X). We discuss Levi-flat domains in surfaces. If Z is a real algebraic hypersurface in P-2, (resp a real-analytic hypersurface with a point of strict pseudoconvexity), then there is a strictly psh function in a neighborhood of Z.
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