2018/05/27 by Huabin Ge, Bobo Hua, Ge, Huabin +1
Computer Science · Mathematics · #51M10 #52C17 #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1805.10643
openalex publication_date 2018/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. For a triangulation of a 3-manifold, we prove that if the number of tetrahedra incident to each vertex is at least 23, then there exist real or virtual ball packings with vanishing (extended) combinatorial scalar curvature, i.e. the (extended) solid angle at each vertex is equal to 4π. In this case, if such a ball packing is real, then the (extended) combinatorial Yamabe flow converges exponentially fast to that ball packing. Moreover, we prove that there is no real or virtual ball packing with vanishing (extended) combinatorial scaler curvature if the number of tetrahedra incident to each vertex is at most 22.