The main result is that for a connected hyperbolic complete Kähler manifold with bounded geometry of order two and exactly one end, either the first compactly supported cohomology with values in the structure sheaf vanishes or the manifold admits a proper holomorphic mapping onto a Riemann surface.
Le résultat principal est que pour une variété kählérienne complète hyperbolique connexe à géométrie bornée d’ordre deux qui a exactement un bout, soit la première cohomologie à valeurs dans le faisceau structural s’annule, ou alors la variété admet une application propre holomorphe dans une surface de Riemann.
Revised:
Accepted:
Published online:
Keywords: Green’s function, pluriharmonic
Mot clés : fonction de Green, pluriharmonique
@article{AIF_2016__66_1_239_0,
author = {Napier, Terrence and Ramachandran, Mohan},
title = {The {Bochner{\textendash}Hartogs} dichotomy for bounded geometry hyperbolic {K\"ahler} manifolds},
journal = {Annales de l'Institut Fourier},
pages = {239--270},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {1},
year = {2016},
doi = {10.5802/aif.3011},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3011/}
}
TY - JOUR AU - Napier, Terrence AU - Ramachandran, Mohan TI - The Bochner–Hartogs dichotomy for bounded geometry hyperbolic Kähler manifolds JO - Annales de l'Institut Fourier PY - 2016 SP - 239 EP - 270 VL - 66 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3011/ DO - 10.5802/aif.3011 LA - en ID - AIF_2016__66_1_239_0 ER -
%0 Journal Article %A Napier, Terrence %A Ramachandran, Mohan %T The Bochner–Hartogs dichotomy for bounded geometry hyperbolic Kähler manifolds %J Annales de l'Institut Fourier %D 2016 %P 239-270 %V 66 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3011/ %R 10.5802/aif.3011 %G en %F AIF_2016__66_1_239_0
Napier, Terrence; Ramachandran, Mohan. The Bochner–Hartogs dichotomy for bounded geometry hyperbolic Kähler manifolds. Annales de l'Institut Fourier, Volume 66 (2016) no. 1, pp. 239-270. doi : 10.5802/aif.3011. https://aif.centre-mersenne.org/articles/10.5802/aif.3011/
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