Code for article: "Piecewise flat Ricci flow of compact without boundary three-manifolds"

2018/05/31 by Rory Conboye, Conboye, Rory
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #53A70 #53E20 #57Q15 #65D18 #Computer Graphics and Visualization Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1806.00095

openalex publication_date 2018/05/31 · openalex created_date 2018/06/13 · openalex updated_date 2026/07/28

Abstract

Mathematica Notebooks containing computations for the article "Piecewise flat Ricci flow of compact without boundary three-manifolds", and data files generated by these notebooks. The Notebooks include: "PFRF1_TriangA" and "PFRF1_TriangB_Nil3", determining the triangulations and intial geometric data for each manifold; "PFRF2_EvolutionsA_Nil3", "PFRF2_EvolutionsB_Gowdy", "PFRF2_EvolutionsC_Torus" and "PFRF2_EvolutionsD_Pert", evolving the piecewise flat Ricci flow for each manifold using the Euler method, along with analysis of the results, and code for producing the graphs that appear in the article; "PFRF0_SmoothRF_Gowdy", solving the reduced PDEs for the smooth Ricci flow of the Gowdy manifold. The remaining zip-file contains the data for each triangulation and evolution generated by the notebooks above. Note: The latest version contains corrections for the boundary identifications of the skew triangulation type for the three-torus initially embedded in four-dimensional Euclidean space.

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