Repositorio
Institucional

Canales Gonzalez, Carolina

LEVI-FLAT HYPERSURFACES AND THEIR COMPLEMENT IN COMPLEX SURFACES

ANNALES INST FOURIER

ANNALES DE L INSTITUT FOURIER

en

In this work we study analytic Levi-flat hypersurfaces in complex algebraic surfaces. First, we show that if this foliation admits chaotic dynamics (i.e. if it does not admit a transverse invariant measure), then the connected components of the complement of the hypersurface are modifications of Stein domains. This allows us to extend the CR foliation to a singular algebraic foliation on the ambient complex surface. We apply this result to prove, by contradiction, that analytic Levi-flat hypersurfaces admitting a transverse affine structure in a complex algebraic surface have a transverse invariant measure. This leads us to conjecture that Levi-flat hypersurfaces in complex algebraic surfaces that are diffeomorphic to a hyperbolic torus bundle over the circle are fibrations by algebraic curves.

Artículo original

10.5802/aif.3139

pdf

complex analysis and complex geometry# theory of foliations# Levi-flat hypersurfaces# invariant measure# Stein manifold# holomorphic convexity# analytic extension

https://aif.centre-mersenne.org/item/AIF_2017__67_6_2423_0/

Mathematics

análisis complejo y geometría compleja# teoría de foliaciones# Hipersuperficies Levi-planas# medida invariante# colector Stein# convexidad holomorfa# extensión analítica

Matemáticas Puras

Matemáticas Aplicadas

Otras Ciencias Naturales

WOS:000428479300004

LEVI-FLAT HYPERSURFACES AND THEIR COMPLEMENT IN COMPLEX SURFACES

Artículo original

version publicada

ANNALES INST FOURIER

ANNALES DE L INSTITUT FOURIER

Matemáticas

0373-0956

en

pdf

diamante#verde

acceso abierto

acceso abierto

CC BY-ND 3.0.

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