Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow
Differential Geometry
2019-12-02 v3
Abstract
In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from initial data.
Keywords
Cite
@article{arxiv.1907.13116,
title = {Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow},
author = {Paula Burkhardt-Guim},
journal= {arXiv preprint arXiv:1907.13116},
year = {2019}
}
Comments
65 pages. v3: small errors corrected. This is a post-peer-review, pre-copyedit version of an article published in Geometric and Functional Analysis. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00039-019-00514-3