The Yau uniformization conjecture asserts that a connected noncompact complex manifold of dimension 
carrying a complete Kähler
metric of positive holomorphic
bisectional curvature is biholomorphic to 
. The curvature is positive
at every point, without a uniform positive lower bound. The conclusion concerns the complex
structure and does not assert that the given metric is Euclidean.
Yau Uniformization Conjecture
See also
Biholomorphic Map, Complete Riemannian Metric, Holomorphic Bisectional Curvature, Kähler Manifold, Kähler MetricExplore with Wolfram|Alpha
References
Liu, G. "On Yau's Uniformization Conjecture." Camb. J. Math. 7, 33-70, 2019. https://doi.org/10.4310/CJM.2019.v7.n1.a2.Cite this as:
Weisstein, Eric W. "Yau Uniformization Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/YauUniformizationConjecture.html