Communications in Analysis and Geometry

Volume 17 (2009)

Number 4

The backward behavior of the Ricci and cross-curvature flows on $\mbox{SL}(2, \mathbb{R})$

Pages: 777 – 796

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n4.a9

Authors

Xiaodong Cao (Department of Mathematics, Cornell University)

John Guckenheimer (Department of Mathematics, Cornell University)

Laurent Saloff-Coste (Department of Mathematics, Cornell University)

Abstract

This paper is concerned with properties of maximal solutions ofthe Ricci and cross-curvature flows on locally homogeneous threemanifolds of type $\mbox{SL}_2(\mathbb R)$. We prove that,generically, a maximal solution originates at a sub-Riemanniangeometry of Heisenberg type. This solves a problem left open inearlier work by two of the authors.

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