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Computational Aspects of Discrete
Minimal Surfaces
Konrad Polthier
Sept. 10, 2002
In differential geometry the study of smooth submanifolds with dis
tinguished curvature properties has a long history and belongs to the
central themes of this Þeld. Modern work on smooth submanifolds,
and on surfaces in particular, relies heavily on geometric and analytic
machinery which has evolved over hundreds of years. However, non
smooth surfaces are also natural mathematical objects, even though
there is less machinery available for studying them. Consider, for ex
ample, the pioneering work on polyhedral surfaces by the Russian
school around Alexandrov [1], or Gromov's approach of doing geom
etry using only a set with a measure and a measurable distance func
tion [10]. Also in other Þelds, for example in computer graphics and
numerics, we nowadays encounter a strong need for a discrete differ
ential geometry of arbitrary meshes.
These tutorial notes introduce the theory and computation of dis
