A finite-time singularity of Calabi flow. 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.
released 2026-09-24 | 4 theorems · 14 lemmas · 20 proofs · 19,900 words |
PLAY LEVEL 1 »(pdf)
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.