Negative Kähler curvature without bounded holomorphic coordinates
What the paper claims, in its own words
Constructs a contractible domain in ℂ3 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 −1 and only constant bounded holomorphic functions; its curvature is not bounded below.
The plain-language explainer for this entry is still coming.
The original papers (2)
- A negatively pinched Kähler threefold without bounded holomorphic coordinates (PDF, opens in a new tab) September 25, 2026 Formal proof listed
- One-sided negative sectional curvature and the holomorphic Liouville property (PDF, opens in a new tab) September 25, 2026