English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study the uniformization conjecture of Yau by using the Gromov-Haudorffconvergence. As a consequence, we confirm Yau's finite generation conjecture.More precisely, on a complete noncompact K\"ahler manifold with nonnegativebisectional curvature, the ring of polynomial growth holomorphic functions isfinitely generated. During the course of the proof, we prove if $M^n$ is acomplete noncompact K\"ahler manifold with nonnegative bisectional curvatureand maximal volume growth, then $M$ is biholomorphic to an affine algebraicvariety. We also confirm a conjecture of Ni on the existence of polynomialgrowth holomorphic functions on K\"ahler manifolds with nonnegative bisectionalcurvature.

Gromov-Hausdorff limit of K\"ahler manifolds and the finite generation conjecture