Work

Integral curvature estimates for solutions to Ricci flow with Lp bounded scalar curvature

Year: 2025

Type: article

Abstract: In this paper we prove localised weighted curvature integral estimates for solutions to the Ricci flow in the setting of a smooth four dimensional Ricci flow or a closed n -dimensional Kähler Ricci flow. These integral estimates improve and extend the integral curvature estimates shown by the second author in an earlier paper. If the scalar curvature is uniformly bounded in the spatial $$L^p$$ L p sense for some $$p>2,$$ p > 2 , then the estimates imply a uniform bound on the spatial $$L^2$$ L 2 norm of the Riemannian curvature tensor. Stronger integral estimates are shown to hold if one further assumes a weak non-inflating condition, or we restrict to closed manifolds.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-025-02250-7

Authors: Jiawei Liu, Miles Simon

Institutions: Nanjing University of Science and Technology, Otto-von-Guericke-Universität Magdeburg

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China, Otto von Guericke University Magdeburg