Work

Ricci-DeTurck flow from rough metrics and applications to scalar curvature problems

Year: 2025

Type: article

Abstract: Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-DeTurck flow starting from rough metrics which are bi-Lipschitz and have small local scaling invariant gradient concentration. As applications, we use the Ricci flow smoothing to show that scalar curvature lower bound is preserved under bi-Lipschitz W 1 , n convergence. This is an counter-part of the celebrated work of Gromov and Bamler. We also use similar idea to study stability problems in scalar curvature geometry.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.110916

Authors: Jianchun Chu, Man-Chun Lee

Institutions: Peking University, Chinese University of Hong Kong

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250