Abstract
Suppose $M$ is a submanifold of ${C^n}$ with real codimension at least one. A geometric description is given of the local hull of holomorphy of an open subset of $M$ which contains a point of higher type in which all Hormander numbers are the same. This result is proved as a consequence of examining the relationship between the hypoanalytic wave front sets of CR functions on $M$ and CR extension to a manifold of one higher dimension than $M$.
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