Reduced distance based at singular time in the Ricci flow

Details Reduced distance based at singular time in the Ricci flow Reduced distance based at singular time in the Ricci flow

2007-11-05

arxiv.org/abs/0711.0558v1

Mathematics

Differential Geometry

17 pages

Scientific paper

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.

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