# Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow

## TL;DR

This paper introduces a new way to define and analyze lower scalar curvature bounds for $C^0$ metrics using regularizing Ricci flow, ensuring stability and preservation of curvature bounds during evolution.

## Contribution

It develops local definitions of weak scalar curvature bounds for $C^0$ metrics and demonstrates their stability and preservation under Ricci flow starting from low-regularity initial data.

## Key findings

- Definitions are stable under higher-order metric perturbations
- Existence of Ricci flow from $C^0$ initial data that becomes smooth for positive times
- Weak scalar curvature bounds are preserved under Ricci flow from $C^0$ metrics

## Abstract

In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ 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 $C^0$ 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 $C^0$ initial data.