There is a contractible complex three-dimensional domain with a complete Kähler metric whose real sectional curvatures lie between two negative constants, yet it has no bounded holomorphic map to complex three-space with nowhere-vanishing Jacobian and is not biholomorphic to a bounded domain.
There is a contractible complex three-dimensional domain with a complete Kähler metric whose real sectional curvatures lie between two negative constants, yet it has no bounded holomorphic map to complex three-space with nowhere-vanishing Jacobian and is not biholomorphic to a bounded domain.
There is a contractible complex three-dimensional domain with a complete Kähler metric whose real sectional curvatures lie between two negative constants, yet it has no bounded holomorphic map to complex three-space with nowhere-vanishing Jacobian and is not biholomorphic to a bounded domain.
If correct, answers the two-sided negatively pinched Kähler uniformization question negatively.
Does two-sided negative curvature force bounded holomorphic coordinates on a complete Kähler manifold?
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OpenAI reports a pinched Kähler threefold without bounded coordinates
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