Dimensional reduction and the long-time behavior of Ricci flow

Lott, John

doi:10.4171/CMH/203

Commentarii Mathematici Helvetici

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Volume 85, Issue 3, 2010, pp. 485–534

DOI: 10.4171/CMH/203

Published online: 2010-05-23

Dimensional reduction and the long-time behavior of Ricci flow

John Lott^[1]

(1) University of California, Berkeley, USA

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t⁻¹) and diameter that is O(t^1/2), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.

Keywords: Ricci flow, geometrization

Lott John: Dimensional reduction and the long-time behavior of Ricci flow. Comment. Math. Helv. 85 (2010), 485-534. doi: 10.4171/CMH/203