A combinatorial curvature flow for compact 3manifolds with boundary
Author:
Feng Luo
Journal:
Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 1220
MSC (2000):
Primary 53C44, 52A55
Published electronically:
January 28, 2005
MathSciNet review:
2122445
Fulltext PDF Free Access
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Abstract: We introduce a combinatorial curvature flow for piecewise constant curvature metrics on compact triangulated 3manifolds with boundary consisting of surfaces of negative Euler characteristic. The flow tends to find the complete hyperbolic metric with totally geodesic boundary on a manifold. Some of the basic properties of the combinatorial flow are established. The most important one is that the evolution of the combinatorial curvature satisfies a combinatorial heat equation. It implies that the total curvature decreases along the flow. The local convergence of the flow to the hyperbolic metric is also established if the triangulation is isotopic to a totally geodesic triangulation.
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 E. Kang and J. H. Rubinstein, Ideal triangulations of 3manifolds I, preprint.
 [La1]
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Additional Information
Feng Luo
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 07059
Email:
fluo@math.rutgers.edu
DOI:
http://dx.doi.org/10.1090/S1079676205001423
PII:
S 10796762(05)001423
Received by editor(s):
May 14, 2004
Published electronically:
January 28, 2005
Communicated by:
Tobias Colding
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
