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Displaying similar documents to “Some results on projectively flat affine surfaces”

Cauchy problems for discrete affine minimal surfaces

Marcos Craizer, Thomas Lewiner, Ralph Teixeira (2012)

Archivum Mathematicum

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In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with co-planar discrete harmonic co-normals, which we call discrete improper affine spheres. Within...