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Pseudo-Calabi Flow on Toric Variety
Abstract
In this paper, we prove the long time existence of the pseudo-Calabi flow on a compact toric variety for any Tn-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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BibTeX
@misc{tian2026pseudocalabi,
title = {{Pseudo-Calabi Flow on Toric Variety}},
author = {Junhao Tian and Kai Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34340},
eprint = {2610.34340},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34340},
}
RIS
TY - UNPB
TI - Pseudo-Calabi Flow on Toric Variety
AU - Junhao Tian
AU - Kai Zheng
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34340
UR - https://arxiv.org/abs/2610.34340
AB - 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.
ER -