论文标题
伪造域在投影空间中具有光滑边界
Pseudoconvex domains with smooth boundary in projective spaces
论文作者
论文摘要
给定pseudoconvex域u具有p^n，n> 2中的c^1边界，我们表明，如果h^{2n-2} _ \ dr}（u）\ not = 0，则在边界U邻居中有一个严格的psh功能，那么我们还可以在x = p^n \ u上求解\ dbar-equare（for Data in for Data in for Data）。在表面。如果z是p^2中的真实代数性超曲面（重新分析的超脉冲，具有严格的伪有点的点），则在Z附近具有严格的PSH函数。
Given a pseudoconvex domain U with C^1-boundary in P^n, n>2, we show that if H^{2n-2}_\dR}(U)\not=0, then there is a strictly psh function in a neighborhood of boundary U. We also solve the \dbar-equation in X=P^n\ U, for data smooth (0,1) forms on X. We also 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.
