Advanced Search

This paper is concerned with (weakly) pseudoconvex real analytic hypersurfaces in ${𝐂}^n$. We are motivated by the study of local boundary regularity of the $\overline{\partial }$-Neumann problem. Subelliptic estimates in a neighborhood of a point $P$ in the boundary (which imply regularity) are controlled by ideals of germs of real analytic functions $I^1(P),\mathrm{\cdots },I^{n-1}(P)$. These ideals have the property that a subelliptic estimate holds for $(p,q)$-forms in a neighborhood of $P$ if and only if $1\in I^q(P)$. The geometrical meaning of this is that $1\in I^q(P)$ if and only...