Boundary Value Problems on Planar Graphs and Flat Surfaces with integer cone singularities, II: The mixed Dirichlet-Neumann Problem

@article{Hersonsky2010BoundaryVP,
  title={Boundary Value Problems on Planar Graphs and Flat Surfaces with integer cone singularities, II: The mixed Dirichlet-Neumann Problem},
  author={Sa'ar Hersonsky},
  journal={arXiv: Differential Geometry},
  year={2010}
}
  • Sa'ar Hersonsky
  • Published 31 May 2010
  • Mathematics
  • arXiv: Differential Geometry
In this paper we continue the study started in part I (posted). We consider a planar, bounded, $m$-connected region $\Omega$, and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$ be a cellular decomposition of $\Omega\cup\bord\Omega$, 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 special type of a (possibly immersed) genus $(m-1)$ singular flat surface, tiled by rectangles and $f$ is… 
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Abstract Consider a planar, bounded, m-connected region Ω, and let ∂Ω be its boundary. Let 𝒯 be a cellular decomposition of Ω ∪ ∂Ω, where each 2-cell is either a triangle or a quadrilateral. From
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