Geodesic
Gromov-Hausdorff limits of Kähler manifolds and the finite generation conjecture
Gang Liu1
1 Northwestern University, Evanston, IL
Annals of mathematics, Tome 184 (2016) no. 3, pp. 775-815.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We study the uniformization conjecture of Yau by using the Gromov-Hausdorff convergence. As a consequence, we confirm Yau’s finite generation conjecture. More precisely, on a complete noncompact Kähler manifold with nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated. During the course of the proof, we prove if $M^n$ is a complete noncompact Kähler manifold with nonnegative bisectional curvature and maximal volume growth, then $M$ is biholomorphic to an affine algebraic variety. We also confirm a conjecture of Ni on the existence of polynomial growth holomorphic functions on Kähler manifolds with nonnegative bisectional curvature.
DOI : 10.4007/annals.2016.184.3.4

Gang Liu 1

1 Northwestern University, Evanston, IL 
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     title = {Gromov-Hausdorff limits of {K\"ahler} manifolds and the finite generation conjecture},
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Gang Liu. Gromov-Hausdorff limits of Kähler manifolds and the finite generation conjecture. Annals of mathematics, Tome 184 (2016) no. 3, pp. 775-815. doi : 10.4007/annals.2016.184.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.3.4/

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