A finite-time singularity of Calabi flow

What OpenAI claims

Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth U(10)-invariant Kähler metric on ℂℙ¹⁰ 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.

Paper

1. A finite-time singularity of Calabi flow on projective space

   24 September 2026 · Preprint, not peer reviewed · PDF

   We construct a smooth Kähler metric in the Fubini–Study class of ℂℙ¹⁰ 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.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.