Yau's uniformization conjecture

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Yau 1982, Survey on PDE in differential geometry (Ann. of Math. Stud. 102) evidence for this event

Yau's uniformization conjecture evidence for this event

Theorem 1.1: if a connected noncompact complex manifold of dimension $n\ge1$ carries a smooth complete Kahler metric with pointwise strictly positive holomorphic bisectional curvature, then it is biholomorphic to $\mathbb C^n$; no curvature bounds, volume growth, noncollapsing or topological hypotheses are assumed. The proof runs a Kahler-Ricci flow built from exhaustions, proves Harnack inequalities by a disc-minimization argument, obtains shrinking holomorphic charts and assembles them by polynomial-automorphism dynamics into a biholomorphism onto all of $\mathbb C^n$. It does not say the metric is flat, and it does not treat nonnegative curvature. parent of this event

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Yau's uniformization conjecture parent of this event