Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive

Bertrand Deroin

doi:10.1016/j.ansens.2004.10.004

Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive

Bertrand Deroin

University of Toronto

Research output: Contribution to journal › Article › peer-review

Abstract

We show that there is no immersed compact Levi-flat hypersurface of class C¹ in the complex projective plane, if the foliation by holomorphic curves carries a harmonic current which is absolutely continuous with respect to the Lebesgue measure, with a density bounded from above and below. This is a corollary of a rigidity result for immersed compact Levi-flat hypersurfaces in complex surfaces of non-negative curvature.

Original language	French
Pages (from-to)	57-75
Number of pages	19
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	38
Issue number	1
DOIs	https://doi.org/10.1016/j.ansens.2004.10.004
Publication status	Published - 1 Jan 2005
Externally published	Yes

Access to Document

10.1016/j.ansens.2004.10.004

Cite this

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abstract = "We show that there is no immersed compact Levi-flat hypersurface of class C1 in the complex projective plane, if the foliation by holomorphic curves carries a harmonic current which is absolutely continuous with respect to the Lebesgue measure, with a density bounded from above and below. This is a corollary of a rigidity result for immersed compact Levi-flat hypersurfaces in complex surfaces of non-negative curvature.",

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AB - We show that there is no immersed compact Levi-flat hypersurface of class C1 in the complex projective plane, if the foliation by holomorphic curves carries a harmonic current which is absolutely continuous with respect to the Lebesgue measure, with a density bounded from above and below. This is a corollary of a rigidity result for immersed compact Levi-flat hypersurfaces in complex surfaces of non-negative curvature.

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