A combinatorial Yamabe problem on two and three dimensional manifolds

Abstract

In this paper, we introduce a new combinatorial curvature on two and three dimensional triangulated manifolds, which transforms in the same way as that of the smooth scalar curvature under scaling of the metric and could be used to approximate the Gauss curvature on two dimensional manifolds. Then we use the flow method to study the corresponding constant curvature problem, which is called combinatorial Yamabe problem.

We add a proof of the discrete maximal principle in this version

References in corpus (6)

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• Geometric triangulations and discrete Laplacians on manifolds
• A discrete uniformization theorem for polyhedral surfaces II
• An extended correction to ``Combinatorial Scalar Curvature and Rigidity of Ball Packings,'' (by D. Cooper and I. Rivin)
• On exterior calculus and curvature in piecewise-flat manifolds
• Combinatorial Calabi flows on surfaces

Cited by in corpus (6)

• On the deformation of inversive distance circle packings, II
• $\alpha$-curvatures and $\alpha$-flows on low dimensional triangulated manifolds
• On the deformation of ball packings
• On the global rigidity of sphere packings on 3-dimensional manifolds
• Rigidity of inversive distance circle packings revisited
• On a combinatorial curvature for surfaces with inversive distance circle packing metrics