Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth U(10)-invariant Kähler metric on \mathbb{CP}^{10} whose flow develops a finite-time singularity. The metric lies in the Fubini–Study class, so the failure occurs even in a class containing a constant-scalar-curvature metric.
Manuscript
A finite-time singularity of Calabi flow on projective space
September 24, 2026 · source · cite as \cite{OAI:A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026}
We construct a smooth Kähler metric in the Fubini–Study class of \mathbb{CP}^{10} whose Calabi flow develops unbounded scalar curvature in finite time. This disproves Chen's smooth long-time existence conjecture, even in a class containing a constant-scalar-curvature metric.
Result 352 · Differential geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md