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

Buckland, John

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

Date

2006

Authors

Buckland, John

Publisher

American Mathematical Society

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.