Defining Pointwise Lower Scalar Curvature Bounds for $C^0$ Metrics with Regularization by Ricci Flow
Differential Geometry
2020-12-18 v3
Abstract
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 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.
Keywords
Cite
@article{arxiv.2007.14967,
title = {Defining Pointwise Lower Scalar Curvature Bounds for $C^0$ Metrics with Regularization by Ricci Flow},
author = {Paula Burkhardt-Guim},
journal= {arXiv preprint arXiv:2007.14967},
year = {2020}
}
Comments
This paper surveys work on the generalized definition of lower scalar curvature bounds for $C^0$ metrics given in arXiv:1907.13116, and states some more streamlined results