2009/12/03 by Sa'ar Hersonsky, Hersonsky, Sa'ar
Mathematics · #53C43 #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:53C43 #msc:57M50
paper · pdf · doi:10.48550/arxiv.0912.0740
27 pages, 11 figures; v2 - revised definition (now denoted by the flux-gradient metric (1.9)) in section 1 and minor modifications of proofs; corrected typos
arxiv created 2010/05/26 · arxiv updated 2010/05/27
Consider a planar, bounded, m-connected region Ω, and let \bordΩ be its boundary. Let T be a cellular decomposition of Ω∪\bordΩ, where each 2-cell is either a triangle or a quadrilateral. From these data and a conductance function we construct a canonical pair (S,f) where S is a genus (m-1) singular flat surface tiled by rectangles and f is an energy preserving mapping from \mathcal T(1) onto S.