Ricci measure for some singular Riemannian metrics

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.

final version

References in corpus (6)

• Ricci flow on surfaces with conic singularities
• Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces
• Singular Kahler-Einstein metrics
• The conical Kähler-Ricci flow on Fano manifolds
• The Ricci flow on the sphere with marked points
• Canonical smoothing of compact Alexandrov surfaces via Ricci flow