## The Andreotti Grauert vanishing theorem for dihedrons of $\Bbb C^n$

J. Math. Sci. Univ. Tokyo
Vol. 2 (1995), No. 1, Page 233--246.

Zampieri, Giuseppe
The Andreotti Grauert vanishing theorem for dihedrons of $\Bbb C^n$
Let $X$ be a complex manifold, $\OX$ the sheaf of analytic functions on $X$, $W$ an open set of $X$ with $C^2$-boundary $M=\partial W$ ($W$ locally on one side of $M$), $z_o$ a point of $M$, $p_o$ the exterior conormal to $W$ at $z_o\,$. If the number of negative eigenvalues for the Levi form of $M$ in a neighborhood of $p_o$ is $\geq s^-$ (resp. $\equiv s^-$), then vanishing of local cohomology groups of $\OX$ over $W$ in degree \$