Short-time existence of solutions to the cross curvature flow on 3-manifolds
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- by John A. Buckland
- Proc. Amer. Math. Soc. 134 (2006), 1803-1807
- DOI: https://doi.org/10.1090/S0002-9939-05-08204-3
- Published electronically: December 16, 2005
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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.References
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Bibliographic 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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1803-1807
- MSC (2000): Primary 53C44, 35K55
- DOI: https://doi.org/10.1090/S0002-9939-05-08204-3
- MathSciNet review: 2207496