On the Smoothness of Levi-foliations
نویسندگان
چکیده
D.E . BARRETT AND J . E . FORNAESS We study the regularity of the induced foliation of a Levi-flat hypersurface in C'° , showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question .
منابع مشابه
Singular Levi-flat Hypersurfaces and Codimension One Foliations
We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular
متن کاملOn the Dynamics of Codimension One Holomorphic Foliations with Ample Normal Bundle
We investigate the accumulation to singular points of leaves of codimension one foliations whose normal bundle is ample, with emphasis on the nonexistence of Levi-flat hypersurfaces.
متن کاملA Characterization of Hyperbolic Kato Surfaces
We give a characterization of hyperbolic Kato surfaces in terms of the existence of an automorphic Green function on a cyclic covering. This is achieved by analysing a naturally defined Levi-flat foliation, and by perturbing certain Levi-flat leaves to strictly pseudoconvex hypersurfaces. 2010 Mathematics Subject Classification: Kato surfaces, Levi-flat foliations, plurisubharmonic functions.
متن کاملHolomorphic Motion of Circles through Affine Bundles
The pivotal topic of this paper is the study of Levi-flat real hypersurfaces S with circular fibers in a rank 1 affine bundle A over a Riemann surface X. (To say that S is Levi-flat is to say that S admits a foliation by Riemann surfaces; equivalently, in the language of [SuTh], S may be said to prescribe a holomorphic motion of circles through A.) After setting notation and terminology in §2 w...
متن کاملPartially Hyperbolic Dynamical Systems
15 3. Stable and unstable filtrations 17 3.1. Existence and subfoliation 17 3.2. Absolute continuity 19 4. Central Foliations 21 4.1. Normal hyperbolicity 21 4.2. Integrability of the central foliation and dynamical coherence 23 4.3. Smoothness of central leaves via normal hyperbolicity 25 4.4. Robustness of the central foliation 26 5. Intermediate Foliations 27 5.1. Nonintegrability of interme...
متن کامل