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A finite-time singularity of Calabi flow
Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth -invariant Kähler metric on 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
Sep 24, 2026·paper.pdf
We construct a smooth Kähler metric in the Fubini–Study class of 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.