Animation of Scherk's first and second surface transforming into each other: they are members of the same associate family of minimal surfaces.
In mathematics, a Scherk surface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834;[1] his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces (the first two were the catenoid and helicoid).[2] The two surfaces are conjugates of each other.
Scherk surfaces arise in the study of certain limiting minimal surface problems and in the study of harmonic diffeomorphisms of hyperbolic space.
^H.F. Scherk, Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen, Journal für die reine und angewandte Mathematik, Volume 13 (1835) pp. 185–208 [1]
mathematics, a Scherksurface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834;...
examples of minimal surface are known explicitly, such as the catenoid, the helicoid, the Scherksurface and the Enneper surface. There has been extensive...
Heinrich Ferdinand Scherk (27 October 1798 – 4 October 1885) was a German mathematician notable for his work on minimal surfaces and the distribution...
triply periodic surface of particular interest for liquid crystal structure the Saddle tower family: generalisations of Scherk's second surface Costa's minimal...
of surfaces, K3 surfaces form one of the four classes of minimal surfaces of Kodaira dimension zero. A simple example is the Fermat quartic surface x 4...
minimal surface family generalizing the singly periodic Scherk's second surface so that it has N-fold (N > 2) symmetry around one axis. These surfaces are...
theoretical appeal of its asymptotic freedom). In 1974, John H. Schwarz and Joël Scherk, and independently Tamiaki Yoneya, studied the boson-like patterns of string...
theory is eleven. In the same year, Eugene Cremmer, Bernard Julia, and Joël Scherk of the École Normale Supérieure showed that supergravity not only permits...
different hypergeometric series, known as contiguity relations. The Kummer surface results from taking the quotient of a two-dimensional abelian variety by...
discuss][clarification needed] The classic 1976 work of Ferdinando Gliozzi, Joël Scherk and David Olive paved the way to a systematic understanding of the rules...
people––is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string...
Riemann surface and a certain four-dimensional SU(2) gauge theory obtained by compactifying the 6D (2,0) superconformal field theory on the surface. The...
important open problem, and only special cases such as moduli spaces of K3 surfaces or Abelian varieties are understood. Another important moduli problem is...
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