Wu's bounded-domain question for negatively pinched Kahler manifolds: is a complete simply connected Kahler manifold with pinched negative curvature biholomorphic to a bounded domain?

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Wu's bounded-domain question for negatively pinched Kahler manifolds: is a complete simply connected Kahler manifold with pinched negative curvature biholomorphic to a bounded domain? evidence for this event

Wu's bounded-domain question for negatively pinched Kahler manifolds: is a complete simply connected Kahler manifold with pinched negative curvature biholomorphic to a bounded domain? parent of this event

Theorem 1.1: there is a contractible domain $M\subset\mathbb C^3$ (a Hartogs-type disc bundle over the unit ball of $\mathbb C^2$) with a smooth complete Kahler metric whose real sectional curvatures satisfy $-B\le K\le -A<0$, such that no bounded holomorphic map $M\to\mathbb C^3$ has nowhere-vanishing Jacobian; hence $M$ is not biholomorphic to any bounded domain. This disproves Wu-Yau Conjecture 4.3 and gives a negative answer under the hypotheses of Wu's 1967 question. It does not show absence of bounded holomorphic functions (two base coordinates are bounded), and the example is Stein. Only complex dimension three is constructed. parent of this event

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Companion: One-sided negative sectional curvature and the holomorphic Liouville property evidence for this event

Lean proof (OAI.PinchedHartogs.main_theorem) evidence for this event

Wu and Yau, Some negatively curved complex geometry (2019 survey), Conjecture 4.3 evidence for this event

VibeMathed record: Wu's bounded-domain question for negatively pinched Kahler manifolds: is a complete simply connected Kahler manifold with pinched negative curvature biholomorphic to a bounded domain? evidence for this event