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Uniqueness Theorems for CR Functions

✍ Scribed by Gerd Schmalz

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
493 KB
Volume
156
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let M be a CR manifold embedded in β„­^s^ of arbitrary codimension. M is called generic if the complex hull of the tangent space in all points of M is the whole β„­^s^. M is minimal (in sense of Tumanov) in p Ο΅ M if there does not exist any CR submanifold of M passing through p with the same CR dimension as M but of smaller dimension. Let M be generic and minimal in some point p Ο΅ M and N be a generic submanifold of M passing through p. We prove that a continuous CR function on M vanishes identically in some neigbourhood of p if its restriction to N either vanishes in p faster then some function with non‐integrable logarithm or it vanishes on a subset of N of positive measure.

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