Work

Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants

Year: 2026

Type: preprint

Abstract: We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.05217

Authors: Li, Haozhao, Wang, Bing, Zheng, Kai

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, University of Science and Technology of China

Awards: G7127922358, G8471289706

OpenAlex ID: W7220716184

Cites: 2

Cited by: 3

Related to: 10