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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Français
Pages (de - à)	57-75
Nombre de pages	19
journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	38
Numéro de publication	1
Les DOIs	https://doi.org/10.1016/j.ansens.2004.10.004
état	Publié - 1 janv. 2005
Modification externe	Oui

Accès au document

10.1016/j.ansens.2004.10.004

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Contient cette citation

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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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