Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Huang, Liding, Zhu, Xiaohua
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5886962956
OpenAlex ID: W7220718075