Ricci measure for some singular Riemannian metrics
John Lott

TL;DR
This paper introduces a measure-based Ricci curvature for specific singular Riemannian metrics, providing a new way to analyze curvature in singular geometric settings and proposing a weak Ricci flow concept.
Contribution
It defines Ricci curvature as a measure for singular torsion-free connections and introduces a weak Ricci flow framework for such manifolds.
Findings
Ricci measure can be explicitly computed in key examples
A new integral formula for Ricci curvature in singular contexts
Proposes a weak Ricci flow solution concept
Abstract
We define the Ricci curvature, as a measure, for certain singular torsion-free connections on the tangent bundle of a manifold. The definition uses an integral formula and vector-valued half-densities. We give relevant examples in which the Ricci measure can be computed. In the time dependent setting, we give a weak notion of a Ricci flow solution on a manifold.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds
