A combinatorial curvature flow for compact 3-manifolds with boundary

By Feng Luo. 2004

54 citations recorded by the source corpus.

We introduce a combinatorial curvature flow for PL 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 ones is that the evolution of the PL 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ec976dba03b101fc39ed8ccbdc511b59364c4cde

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In Applied Mathematics

1. Xu Xu
2. Huabin Ge

In Geometry and Topology

1. Xu Xu
2. Huabin Ge
3. Michael Schwarz
4. Matthias Keller

Citations in the corpus

• Discrete quasi-Einstein metrics and combinatorial curvature flows in 3-dimension (2013, background): “In [13], Feng Luo suggested finding a good parametrization so as the admissible space of metrics became convex in the new coordinate.”