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A combinatorial curvature flow for compact 3-manifolds with boundary


Author: Feng Luo
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 12-20
MSC (2000): Primary 53C44, 52A55
DOI: https://doi.org/10.1090/S1079-6762-05-00142-3
Published electronically: January 28, 2005
MathSciNet review: 2122445
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Abstract: We introduce a combinatorial curvature flow for piecewise constant curvature metrics on compact triangulated 3-manifolds 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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Additional Information

Feng Luo
Affiliation: Department of Mathematics, Rutgers University, Piscataway, NJ 07059
Email: fluo@math.rutgers.edu

DOI: https://doi.org/10.1090/S1079-6762-05-00142-3
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.

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