English

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 C0C^0 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 C0C^0 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 C0C^0 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