Conformal Bach flow

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-03-30 DOI:10.1007/s10455-023-09897-x

Jiaqi Chen, Peng Lu, Jie Qing

引用次数: 0

Abstract

In this article we introduce conformal Bach flow and establish its well-posedness on closed manifolds. We also obtain its backward uniqueness. To give an attempt to study the long-time behavior of conformal Bach flow, assuming that the curvature and the pressure function are bounded, global and local Shi’s type \(L^2\)-estimate of derivatives of curvatures is derived. Furthermore, using the \(L^2\)-estimate and based on an idea from (Streets in Calc Var PDE 46:39–54, 2013) we show Shi’s pointwise estimate of derivatives of curvatures without assuming Sobolev constant bound.

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保形巴赫流

本文引入保角巴赫流，并建立了它在闭流形上的适定性。我们也获得了它向后的独特性。为了尝试研究保角巴赫流的长期行为，假设曲率和压力函数是有界的，导出了曲率导数的全局和局部施型（L^2）估计。此外，使用\（L^2）-估计，并基于（Streets in Calc Var PDE 46:39–541013）中的一个想法，我们展示了施对曲率导数的逐点估计，而不假设Sobolev常数界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.