What was already known
Yau asked whether a complete simply connected Kähler manifold with a uniform negative upper sectional-curvature bound must admit a nonconstant bounded holomorphic function. A separate pinched threefold concerns bounded coordinate systems and retains nonconstant bounded functions.
AI involvement
OpenAI lists this manuscript as model-produced and OpenAI-authored. The release does not identify a human who completed a check or explained this construction.
The institutionally credited OpenAI model produced the selected construction; contribution-specific autonomy beyond that is undocumented.
Importance
The example answers the one-sided bounded-holomorphic-function question negatively in sufficiently high complex dimension.
Limitations
The exact fixed dimension and full assumptions need direct mathematical review. The Lean formalization for the separate pinched threefold does not check this one-sided holomorphic Liouville example.
Technical verification
The one-sided theorem is reported in the manuscript map. The available Lean scope note expressly covers the separate pinched threefold, so its machine check cannot be transferred to this one-sided, only-constant-functions claim. No completed check of the selected theorem is documented.
Human understanding
No named human explanation of the construction's holomorphic Liouville mechanism is documented. Few is the missing-evidence default.
Correction and publication history
If correct, the example answers the one-sided bounded-holomorphic-function question negatively in sufficiently high complex dimension.
Read this published revision