Short-time existence of solutions to the cross curvature flow on 3-manifolds

Buckland, John

doi:10.1090/S0002-9939-05-08204-3

Short-time existence of solutions to the cross curvature flow on 3-manifolds
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by John A. Buckland PDF

Proc. Amer. Math. Soc. 134 (2006), 1803-1807 Request permission

Abstract:

Given a compact 3-manifold with an initial Riemannian metric of positive (or negative) sectional curvature, we prove the short-time existence of a solution to the cross curvature flow. This is achieved using an idea first introduced by DeTurck (1983) in his work establishing the short-time existence of solutions to the Ricci flow.

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