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arXiv · 2610.34340

Pseudo-Calabi Flow on Toric Variety

Junhao Tian·Kai Zheng
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Abstract

In this paper, we prove the long time existence of the pseudo-Calabi flow on a compact toric variety for any $T^n$-invariant initial Kähler metric. If the Mabuchi functional is proper modulo automorphisms, the flow converges exponentially to a constant scalar curvature Kähler (cscK) metric. In particular, this gives a flow proof that properness of the K-energy implies the existence of a cscK metric in the toric setting.

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Junhao Tian, Kai Zheng. 2026-10-25. Pseudo-Calabi Flow on Toric Variety. https://arxiv.org/abs/2610.34340

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