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arXiv · 2610.05201

Convergence of Generalized Kähler--Ricci Flow on Toric Fano Manifolds

Liding Huang·Xiaohua Zhu
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Abstract

We first define an extended Mabuchi functional for a class of generalized Kähler metrics of symplectic type on a toric Fano manifold $(M,J,\mathbb{T})$, and prove it is proper. Then by showing the monotonicity of functional along the normalized generalized Kähler-Ricci flow for any initial $\mathbb{T}$-invariant generalized Kähler metric with its symplectic form in $2πc_1(M,J)$, we prove that the flow converges to a Kähler-Ricci soliton. The result confirms a conjecture of Apostolov-Streets-Ustinovskiy.

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Liding Huang, Xiaohua Zhu. 2026-10-04. Convergence of Generalized Kähler--Ricci Flow on Toric Fano Manifolds. https://arxiv.org/abs/2610.05201

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