{"id":"openai-math/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates","pdf":"https://github.com/openai/math/blob/main/preprints/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-negatively-pinched-Kahler-threefold-without-bounded-holomorphic-coordinates-September-25-2026","tags":["complex-geometry","kahler-geometry","uniformization"],"score":0,"title":"A negatively pinched Kähler threefold without bounded holomorphic coordinates","domain":"Differential geometry","family":"359","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We construct a contractible domain in complex dimension three with a complete Kähler metric whose real sectional curvatures lie between two finite negative constants. It admits no bounded holomorphic map to ℂ 3 with nowhere-vanishing Jacobian and is therefore not biholomorphic to a bounded domain. This gives a negative answer to the negatively pinched Kähler uniformization question.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"Negative Kähler curvature without bounded holomorphic coordinates"}