PreprintarXiv licencearXiv
On global Chern-Calabi flows on compact complex surfaces
Abstract
In this paper, we propose the Chern-Calabi Flow for extremal metrics in conformal Hermitian geometry. After the existence of extremal metric, we consider the existence of global flows to the Chern-Calabi flows for extremal metrics on compact complex surfaces with Gauduchon metrics. To achieve this goal, we use the Adams inequality and the Gronwall inequality method to obtain fourth order derivative norm estimates. We also study the convergence of the global solution to the Chern-Calabi flow and its limit is the solution of the Chern-Calabi extremal metric problem. We propose a fourth order elliptic problem and derive the Bochner formula relevant to the elliptic estimates for the Chern-Calabi heat flow.
Related
- Positive scalar curvature Kähler cones on compact complex surfaces
- Global C2,α estimate for complex Monge--Ampère equations on compact Kähler manifolds
- Integral Bott--Chern cohomology of Generalized Calabi--Eckmann threefolds
- Chern scalar curvature and finite-time singularities of the conformal Chern--Calabi flow
- Continuation and convergence for the higher dimensional conformal Chern--Calabi flow
BibTeX
@misc{ma2026global,
title = {{On global Chern-Calabi flows on compact complex surfaces}},
author = {Li Ma and Li Sheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31068},
eprint = {2610.31068},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31068},
}
RIS
TY - UNPB
TI - On global Chern-Calabi flows on compact complex surfaces
AU - Li Ma
AU - Li Sheng
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31068
UR - https://arxiv.org/abs/2610.31068
AB - In this paper, we propose the Chern-Calabi Flow for extremal metrics in conformal Hermitian geometry. After the existence of extremal metric, we consider the existence of global flows to the Chern-Calabi flows for extremal metrics on compact complex surfaces with Gauduchon metrics. To achieve this goal, we use the Adams inequality and the Gronwall inequality method to obtain fourth order derivative norm estimates. We also study the convergence of the global solution to the Chern-Calabi flow and its limit is the solution of the Chern-Calabi extremal metric problem. We propose a fourth order elliptic problem and derive the Bochner formula relevant to the elliptic estimates for the Chern-Calabi heat flow.
ER -