Discrete affine minimal surfaces with indefinite metric

Marcos Craizer; Henri Anciaux; Thomas Lewiner

doi:10.1016/j.difgeo.2009.07.004

Discrete Geometry

Discrete affine minimal surfaces with indefinite metric

Marcos Craizer, Henri Anciaux, Thomas Lewiner

Differential Geometry and its Applications 28(2): pp. 158-169 (April 2010)

Discrete affine minimal surfaces with indefinite metric

abstract

Abstract

Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that they are critical points of an affine area functional defined on the space of quadrangular discrete surfaces. The construction makes use of asymptotic coordinates and allows defining the discrete analogs of some differential geometric objects, such as the normal and co normal vector fields, the cubic form and the compatibility equations.

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BibTeX

@article{minaffine_dga,
  author        = {Marcos Craizer and Henri Anciaux and Thomas Lewiner},
  title         = {Discrete affine minimal surfaces with indefinite metric},
  year          = {2010},
  month         = {april},
  journal       = {Differential Geometry and its Applications},
  volume        = {28},
  number        = {2},
  pages         = {158--169},
  publisher     = {Elsevier},
  doi           = {10.1016/j.difgeo.2009.07.004},
  url           = {https://thomas.lewiner.org/pdfs/minaffine_dga.pdf}
}