Dimensional reduction and the long-time behavior of Ricci flow

Abstract

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that decay like the inverse of t and diameter that increases at most like the square root of t, then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.

final version

References in corpus (1)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by in corpus (3)

• Ricci Solitons and Einstein-Scalar Field Theory
• First variation of the Log Entropy functional along the Ricci flow
• Geometric Structures of Collapsing Riemannian Manifolds II: N*-bundles and Almost Ricci Flat Spaces