Defining Pointwise Lower Scalar Curvature Bounds for C0 Metrics with Regularization by Ricci Flow

被引：1

作者：

Burkhardt-Guim, Paula ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2020年 / 16卷

基金：

美国国家科学基金会;

关键词：

Ricci flow; scalar curvature; synthetic lower curvature bounds; MANIFOLDS; DIRECTION;

D O I：

10.3842/SIGMA.2020.128

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We survey some recent work using Ricci flow to create a class of local definitions of weak lower scalar curvature bounds that is well defined for C-0 metrics. We discuss several properties of these definitions and explain some applications of this approach to questions regarding uniform convergence of metrics with scalar curvature bounded below. Finally, we consider the relationship between this approach and some other generalized notions of lower scalar curvature bounds.

引用

页数：10

共 12 条

[1] POINTWISE LOWER SCALAR CURVATURE BOUNDS FOR C0 METRICS VIA REGULARIZING RICCI FLOW
Burkhardt-Guim, Paula
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[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2024, 2024 (806): : 187 - 245
[9] Pointwise lower scalar curvature bounds for C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} metrics via regularizing Ricci flow
Paula Burkhardt-Guim
[J]. Geometric and Functional Analysis, 2019, 29 (6) : 1703 - 1772
[10] Lower bounds for the scalar curvatures of Ricci flow singularity models
Chan, Pak-Yeung
Chow, Bennett
Ma, Zilu
Zhang, Yongjia
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2023, 2023 (794): : 253 - 265

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