The Journal of Geometric Analysis

, Volume 17, Issue 2, pp 321–341

# Nowhere minimal CR submanifolds and Levi-flat hypersurfaces

Article

## Abstract

A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces.

32V40 32C07

## Key Words and Phrases

Singular Levi-flat hypersurfaces CR submanifolds local holomorphic invariants

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