{"id":"openai-math/One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property","pdf":"https://github.com/openai/math/blob/main/preprints/One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/One-sided-negative-sectional-curvature-and-the-holomorphic-Liouville-property-September-25-2026","tags":["complex-geometry","riemannian-geometry","several-complex-variables"],"score":0,"title":"One-sided negative sectional curvature and the holomorphic Liouville property","domain":"Differential geometry","family":"359","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We construct, in some sufficiently large fixed finite complex dimension m , a domain in ℂ m 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Negative Kähler curvature without bounded holomorphic coordinates"}