Abstract
In this paper we continue the study started in Hersonsky (in press) [16]. We 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 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 an energy preserving mapping from T(1) onto S. In Hersonsky (in press) [16] the solution of a Dirichlet problem defined on T(0) was utilized, in this paper we employ the solution of a mixed Dirichlet-Neumann problem.
Original language | English |
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Pages (from-to) | 329-347 |
Number of pages | 19 |
Journal | Differential Geometry and its Applications |
Volume | 29 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jun 2011 |
Externally published | Yes |
Keywords
- Flat surfaces with conical singularities
- Harmonic functions on graphs
- Planar networks
- Primary
- Secondary
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Computational Theory and Mathematics