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Differential Geometry III:
Minimal Surfaces: Classical and Discrete

(Summer 2013)

Lectures Alexander Bobenko Mon 14-16 MA 848
Tue 14-16 MA 848

This is a course of the Berlin Mathematical School held in English.

Contents

Theory of Minimal Surfaces, classical and discrete. This theory is a meeting point of differential geometry of surfaces, complex analysis, theory of Riemann surfaces and discrete differential geometry. We will learn local and global geometric properties of minimal surfaces, their analytic description, famous classical minimal surfaces. Structure preserving discretizations based on discrete curvatures, discrete Laplace-Beltrami operator and discrete Riemann surfaces as well as on circle patterns will be studied.

Literature

  • U. Dierkes, S. Hildebrandt, F. Sauvigny, Minimal surfaces. Grundlehren der Mathematischen Wissenschaften 339. Springer, 2010. xvi+688
  • A.I. Bobenko, T. Hoffmann, B.A. Springborn, Minimal surfaces from circle patterns: Geometry from combinatorics, Ann. of Math. 164:1 (2006) 231-264
  • U. Pinkall, K. Polthier, Computing discrete minimal surfaces and their conjugates. Experiment. Math. 2:1 (1993) 15-36
  • A.I. Bobenko, B.A. Springborn, A discrete Laplace-Beltrami operator for simplicial surfaces, Discrete and Computational Geometry 38:4 (2007) 740-756

Office hours

Office hours Alexander Bobenko Thu 14-15 MA 881

Felix Günther . 09.04.2013.