Buckland, John2016-03-182016-03-180002-9939http://hdl.handle.net/1885/100583Given 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.This research was partially supported by an Australian Research Council Discovery grant entitled Geometric evolution equations and global effects of curvature.© 2005 American Mathematical SocietyNonlinear evolution equationscurvature flowshort-time existence200610.1090/S0002-9939-05-08204-32016-06-14