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Uniqueness Theorems for CR Functions
Author(s) -
Schmalz Gerd
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921560112
Subject(s) - mathematics , submanifold , codimension , dimension (graph theory) , uniqueness , combinatorics , function (biology) , hypersurface , pure mathematics , logarithm , space (punctuation) , mathematical analysis , linguistics , philosophy , evolutionary biology , biology
Let M be a CR manifold embedded in ℭ s of arbitrary codimension. M is called generic if the complex hull of the tangent space in all points of M is the whole ℭ s . M is minimal (in sense of Tumanov) in p ϵ 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 ϵ 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.