Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples
Ulrike Bücking · Birkhäuser Basel eBooks · 2008
We construct discrete solutions to a class of boundary value problems for minimal surfaces without ends, including special classes of Plateau’s problem. The boundary consists of finitely many straight line segments lying on the surface and/or planes intersecting the surface orthogonally. The discrete minimal surfaces which satisfy the given boundary conditions are built from a combinatorial parametrization, using an orthogonal circle pattern which approximates the Gauss map and a discrete duality transformation for S-isothermic surfaces.