2017/03/07 by Maria Trnková
Computer Science · Mathematics · #Algorithm #Applied mathematics #Boundary value problem #Computation #Dirichlet L-function #Dirichlet distribution #Dirichlet eigenvalue #Dirichlet problem #Dirichlet's energy #Dirichlet's principle #Domain (mathematical analysis) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #math.GT #semigroups and automata theory
paper · pdf · doi:10.1016/j.topol.2019.106900
published as Topology and its Applications, Vol. 268 (2019), 106900 · 10 pages, 4 figures
arxiv created 2017/03/07 · openalex publication_date 2019/09/25 · openalex created_date 2019/10/03 · arxiv updated 2019/10/16 · openalex updated_date 2026/08/05
In this paper we address some problems concerning an approximate Dirichlet domain. We show that under some assumptions the approximate Dirichlet domain can work equally well as an exact Dirichlet domain. In particular, we consider a problem of tiling a hyperbolic ball with copies of the Dirichlet domain. This problem arises in the construction of the length spectrum algorithm which is im- plemented by the computer program SnapPea. Our result explains the empirical fact that the program works surprisingly well despite it does not use exact data. Also we demonstrate an improvement in the algorithm for rigorous construction of the length spectrum of a hyperbolic 3-manifold.