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Short-time existence of solutions to the cross curvature flow on 3-manifolds
Author(s):
John
A.
Buckland
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1803-1807.
MSC (2000):
Primary 53C44, 35K55
Posted:
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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- B. Chow and R. Hamilton, The cross curvature flow of 3-manifolds with negative sectional curvature, Turk. J. Math., 28 (2004), 1-10. MR 2055396 (2005a:53107)
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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:
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
Posted:
December 16, 2005
Additional Notes:
This research was partially supported by an Australian Research Council Discovery grant entitled \textit{Geometric evolution equations and global effects of curvature}
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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