Generalisations and Links To Other Fields
Minimal surfaces can be defined in other manifolds than R3, such as hyperbolic space, higher-dimensional spaces or Riemannian manifolds.
The definition of minimal surfaces can be generalized/extended to cover constant-mean-curvature surfaces: surfaces with a constant mean curvature, which need not equal zero.
In Discrete differential geometry discrete minimal surfaces are studied: simplicial complexes of triangles that minimize their area under small perturbations of their vertex positions. Such discretizations are often used to approximate minimal surfaces numerically, even if no closed form expressions are known.
Brownian motion on a minimal surface leads to probabilistic proofs of several theorems on minimal surfaces.
Minimal surfaces have become an area of intense scientific study, especially in the areas of molecular engineering and materials science, due to their anticipated applications in self-assembly of complex materials.
Minimal surfaces play a role in general relativity. The apparent horizon (marginally outer trapped surface) is a minimal hypersurface, linking the theory of black holes to minimal surfaces and the Plateau problem.
Minimal surfaces are part of the generative design toolbox used by modern designers. In architecture there has been much interest in tensile structures, which are closely related to minimal surfaces. A famous example is the Olympiapark in Münich by Frei Otto, inspired by soap surfaces.
In the art world, minimal surfaces have been extensively explored in the sculpture of Robert Engman (1927– ), Robert Longhurst (1949– ), and Charles O. Perry (1929–2011), among others.
Read more about this topic: Minimal Surface
Famous quotes containing the words links and/or fields:
“An alliance is like a chain. It is not made stronger by adding weak links to it. A great power like the United States gains no advantage and it loses prestige by offering, indeed peddling, its alliances to all and sundry. An alliance should be hard diplomatic currency, valuable and hard to get, and not inflationary paper from the mimeograph machine in the State Department.”
—Walter Lippmann (1889–1974)
“As the fields fear drought in autumn, so people fear poverty in old age.”
—Chinese proverb.