Abstract

Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoconcave and two flat (i.e. locally zero sets of pluriharmonic functions) hypersurfaces. Finiteness and vanishing cohomology theorems obtained in [Saracco and Tomassini, Math. Z. 256: 737–748, 2007, Bull. Sci. Math. 132: 232–245, 2008] for semi q-coronae are generalized in this context and lead to results on extension problems and removable sets for sections of coherent sheaves and analytic subsets.