Reduced distance based at singular time in the Ricci flow

Abstract

In this paper, we define a reduced distance function based at a point at the singular time $T<\infty$ of a Ricci flow. We also show the monotonicity of the corresponding reduced volume based at time T, with equality iff the Ricci flow is a gradient shrinking soliton. Our curvature bound assumption is more general than the type I condition.

17 pages

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• On a classification of the gradient shrinking solitons
• On rotationally invariant shrinking gradient Ricci solitons