The Bochner–Hartogs dichotomy for bounded geometry hyperbolic Kähler manifolds
Annales de l'Institut Fourier, Volume 66 (2016) no. 1, p. 239-270

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.

Received : 2014-09-25
Revised : 2015-04-29
Accepted : 2015-05-20
Published online : 2016-02-17
Classification:  32E40
Keywords: Green’s function, pluriharmonic
     author = {Napier, Terrence and Ramachandran, Mohan},
     title = {The Bochner--Hartogs dichotomy for bounded geometry hyperbolic K\"ahler manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {1},
     year = {2016},
     pages = {239-270},
     doi = {10.5802/aif.3011},
     language = {en},
     url = {}
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.

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