A finite-time singularity of Calabi flow

1 paper

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.

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A finite-time singularity of Calabi flow on projective space

OpenAI · 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.

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@misc{OAI:A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026,
  author = {{OpenAI}},
  title = {{A finite-time singularity of Calabi flow on projective space}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026/paper.pdf}{OAI:A-finite-time-singularity-of-Calabi-flow-on-projective-space-September-24-2026}},
  year = {2026}
}

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