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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: John A. Buckland
Journal: Proc. Amer. Math. Soc. 134 (2006), 1803-1807
MSC (2000): Primary 53C44, 35K55
Published electronically: December 16, 2005
MathSciNet review: 2207496
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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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Additional Information

John A. Buckland
Affiliation: Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia
Email: John.Buckland@maths.anu.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08204-3
PII: S 0002-9939(05)08204-3
Keywords: Nonlinear evolution equations, curvature flow, short-time existence
Received by editor(s): January 31, 2005
Received by editor(s) in revised form: February 1, 2005
Published electronically: December 16, 2005
Additional Notes: This research was partially supported by an Australian Research Council Discovery grant entitled Geometric evolution equations and global effects of curvature
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.