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An Introduction to Minimal Surfaces
By Hermann Karcher and Konrad Polthier


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Introduction
Plateau
History
Visualization
Architecture
Crystallography
Weierstraß
Properties 1
Properties 2
Properties 3
Symmetry
Alteration
Periodic
Handles
Production
Scenes 1
Scenes 2
Scenes 3
Results
Exhibition
Numerics
References
Web Links

Minimal History Exhibition

Fig 24. The most important minimal surfaces of the last centuries are displayed in the minimal surface exhibition. Video (15.5MB, 4.2MB)

Two centuries of mathematical research on minimal surfaces is accompanied and determined by the discovery of famous example surfaces. The exhibition of historic minimal surfaces is the first collection of the most influential examples. The exhibition includes the classic catenoid of Euler (1745) and helicoid of Meusnier (1770), Scherk's surface (1835) found as a graph over a square, Enneper's algebraicly given surface (Fig 24), one of the first solutions of a boundary value problem by Schwarz, Riemann's surface in terms of the Weierstraß representation formula, Schoen's triply periodic surfaces in crystallographic cells, Chen-Gackstatter surface of higher genus parameterized using the Weierstraß P-function leading to the discovery of the Costa-Hoffman-Meeks surface, now the most famous piece. Karcher's modification of the Scherk surface and Hoffman-Karcher-Wei's 'Helicoid with a Handle' are representatives of the most fruitful period of the last 15 years and symbolize the current high level of the constructive aspects of minimal surfaces.

© 1996-2013 Last modified: 23.04.2013 --- Konrad Polthier --- Freie Universität Berlin, Germany