# Foliations on the complex projective plane with many parabolic leaves

Annales de l'institut Fourier (1994)

- Volume: 44, Issue: 4, page 1237-1242
- ISSN: 0373-0956

## Access Full Article

top## Abstract

top## How to cite

topBrunella, Marco. "Foliations on the complex projective plane with many parabolic leaves." Annales de l'institut Fourier 44.4 (1994): 1237-1242. <http://eudml.org/doc/75095>.

@article{Brunella1994,

abstract = {We prove that a foliation on $\{\bf C\}P^2$ with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.},

author = {Brunella, Marco},

journal = {Annales de l'institut Fourier},

keywords = {holomorphic foliations; harmonic measures; parabolic Riemann surfaces},

language = {eng},

number = {4},

pages = {1237-1242},

publisher = {Association des Annales de l'Institut Fourier},

title = {Foliations on the complex projective plane with many parabolic leaves},

url = {http://eudml.org/doc/75095},

volume = {44},

year = {1994},

}

TY - JOUR

AU - Brunella, Marco

TI - Foliations on the complex projective plane with many parabolic leaves

JO - Annales de l'institut Fourier

PY - 1994

PB - Association des Annales de l'Institut Fourier

VL - 44

IS - 4

SP - 1237

EP - 1242

AB - We prove that a foliation on ${\bf C}P^2$ with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.

LA - eng

KW - holomorphic foliations; harmonic measures; parabolic Riemann surfaces

UR - http://eudml.org/doc/75095

ER -

## References

top- [Arn] V. I. ARNOL'D, Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Mir, Moscou (1980). Zbl0956.34501MR83a:34003
- [CLS1] C. CAMACHO, A. LINS NETO, P. SAD, Minimal sets of foliations on complex projective spaces, Publ. IHES, 68 (1988), 187-203. Zbl0682.57012MR90e:58129
- [CLS2] C. CAMACHO, A. LINS NETO, P. SAD, Foliations with algebraic limit sets, Ann. of Math., 136 (1992), 429-446. Zbl0769.57017MR93i:32035
- [Gar] L. GARNETT, Foliations, the ergodic theorem and brownian motion, Jour. of Funct. Anal., 51 (1983), 285-311. Zbl0524.58026MR84j:58099
- [Ghy] E. GHYS, Topologie des feuilles génériques, preprint ENS de Lyon (1993). Zbl0843.57026
- [KM] Y. KUSUNOKI, S. MORI, On the harmonic boundary of an open Riemann surface, I, Jap. Jour. of Math., 29 (1959), 52-56. Zbl0098.28002MR22 #11125a
- [Suz] M. SUZUKI, Sur les intégrales premières de certains feuilletages analytiques complexes, Séminaire Norguet, Springer Lect. Notes, 670 (1977), 53-79. Zbl0391.32017MR80h:57038
- [Tsu] M. TSUJI, Potential theory in modern function theory, Maruzen, Tokyo (1959). Zbl0087.28401MR22 #5712
- [Var] N. Th. VAROPOULOS, Random walks on groups. Applications to Fuchsian groups, Ark. för Math., 23 (1985), 171-176. Zbl0596.60073MR87b:60107

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.