  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-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic
functions) hypersurfaces. Finiteness and vanishing cohomology theorems obtained
in math/0503490 and math/0701549 for semi q-coronae are generalized in this
context and lead to results on extension problem and removable sets for
sections of coherent sheaves and analytic subsets.

Complex Variables