Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 359-02. One-sided negative sectional curvature and the holomorphic Liouville property
Manuscript map · lines 9295–9304
OpenAI@2026-10-07#rem:oai-p-359-02
Authors: OpenAI. Family 359.
Title: One-sided negative sectional curvature and the holomorphic Liouville property.
Abstract: We construct, in some sufficiently large fixed finite complex dimension m, a domain in ℂm diffeomorphic to ${}mathbb R{}{2m}$ 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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