On scalar curvature lower bounds and scalar curvature measure

TL;DR

This paper explores the relationship between scalar curvature bounds and distance-decreasing maps, providing conditions for scalar curvature measures to exist in Ricci flow limits.

Contribution

It establishes a connection between scalar curvature bounds and specific maps, and offers a criterion for scalar curvature measure existence in Ricci flow limits.

Findings

Link between scalar curvature bounds and distance-decreasing maps

Sufficient condition for scalar curvature measure in Ricci flow limits

Insights into scalar curvature behavior under geometric flows

Abstract

We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a Ricci flow solution.