OpenAI · 359-02 · 2026-09-25 · Differential geometry
One-sided negative sectional curvature and the holomorphic Liouville property
preprints/One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property-September-25-2026
Family 359. Negative Kähler curvature without bounded holomorphic coordinates.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Constructs a contractible domain in with a complete negatively pinched Kähler metric but no bounded holomorphic coordinates, disproving bounded-domain uniformization in this setting. A higher-dimensional example has sectional curvature at most and only constant bounded holomorphic functions; its curvature is not bounded below.
We construct, in some sufficiently large fixed finite complex dimension m, a domain in ℂm diffeomorphic to that admits a complete Kähler metric with real sectional curvature at most −1 and has only constant bounded holomorphic functions. Its sectional curvatures are unbounded below. The construction gives a negative answer to the one-sided bounded-holomorphic-function question.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
A Lean scope note is stored for family 359, but it does not name this preprint. It names 359-01. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.