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We show that no compact Levi-flat CR manifold of CR codimension one admits a continuous CR function which is nonconstant along leaves of the Levi foliation. We also prove the nonexistence of certain CR functions on a neighborhood of a compact leaf of some Levi-flat CR 3-manifolds, and apply it to showing that some foliated 3-manifolds cannot be embedded as smooth Levi-flat real hypersurfaces in complex surfaces.

Propagation dans les variétés $C R$

J.-M. Trepreau (1989/1990)

Séminaire Équations aux dérivées partielles (Polytechnique)

Quasiconformal equivalence of spherical CR manifolds.

Miner, Robert R. (1994)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

Regularity and extremality of quasiconformal homeomorphisms on CR 3-manifolds.

Tang, Puqi (1996)

Annales Academiae Scientiarum Fennicae. Mathematica

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Stephen S.-T. Yau (2011)

Journal of the European Mathematical Society

Let $X_{1}$ and $X_{2}$ be two compact strongly pseudoconvex CR manifolds of dimension $2 n - 1 \geq 5$ which bound complex varieties $V_{1}$ and $V_{2}$ with only isolated normal singularities in $ℂ^{N 1}$ and $ℂ^{N 2}$ respectively. Let $S_{1}$ and $S_{2}$ be the singular sets of $V_{1}$ and $V_{2}$ respectively and $S_{2}$ is nonempty. If $2 n - N_{2} - 1 \geq 1$ and the cardinality of $S_{1}$ is less than 2 times the cardinality of $S_{2}$ , then we prove that any non-constant CR morphism from $X_{1}$ to $X_{2}$ is necessarily a CR biholomorphism. On the other hand, let $X$ be a compact strongly pseudoconvex CR manifold of...

Necessary topological conditions are given for the closed CR embedding of a CR manifold into a Stein manifold or into a complex projective space.

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A reflection principle on strongly pseudoconvex domains with generic corners.

Algebraic approximation in analytic geometry.

An analogy of Tian-Todorov theorem on deformations of CR-structures

Aneurysms of pseudoconcave CR manifolds.

Cauchy-Riemann functions on manifolds of higher codimension in complex space.

CR-structures on three dimensional circle bundles.

Duality and distribution cohomology of $C R$ manifolds

Instrinsic Connections for Levi Metrics.

Maximally homogeneous nondegenerate CR manifolds.

Microlocal analyticity for ...b in block-decoupled pseudoconvex domains.

New $C R$ invariants and their application to the $C R$ equivalence problem

Non-embeddable CR-manifolds and surface singularities.

On the nonexistence of CR functions on Levi-flat CR manifolds.

Propagation dans les variétés $C R$

Quasiconformal equivalence of spherical CR manifolds.

Regularity and extremality of quasiconformal homeomorphisms on CR 3-manifolds.

Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Sur la propagation des singularités dans les variétés CR

The asymptotic expansion of a CR invariant and Grauert tubes.

The topology of Stein CR manifolds and the Lefschetz theorem

Currently displaying 1 – 20 of 21