Not to be confused with minimal rational surface or minimal algebraic surface.
A helicoid minimal surface formed by a soap film on a helical frame
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below).
The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum.
In mathematics, a minimalsurface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below)...
In differential geometry, the Schwarz minimalsurfaces are periodic minimalsurfaces originally described by Hermann Schwarz. In the 1880s Schwarz and...
triply periodic minimalsurface (TPMS) is a minimalsurface in ℝ3 that is invariant under a rank-3 lattice of translations. These surfaces have the symmetries...
In mathematics, a minimalsurface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose...
molecules results in a minimalsurface area. As a result of surface area minimization, a surface will assume a smooth shape. Surface tension, represented...
Meusnier used it in 1776, in his studies of minimalsurfaces. It is important in the analysis of minimalsurfaces, which have mean curvature zero, and in...
list of surfaces in mathematics. They are divided into minimalsurfaces, ruled surfaces, non-orientable surfaces, quadrics, pseudospherical surfaces, algebraic...
although many more have been discovered. Minimalsurfaces can also be defined by properties to do with surface area, with the consequence that they provide...
The helicoid, also known as helical surface, after the plane and the catenoid, is the third minimalsurface to be known. It was described by Euler in...
produces this minimalsurface of revolution. There are only two minimalsurfaces of revolution (surfaces of revolution which are also minimalsurfaces): the plane...
periodic minimalsurface discovered by Alan Schoen in 1970. It arises naturally in polymer science and biology, as an interface with high surface area. The...
is minimal or minimal genus if there is no other splitting of the ambient three-manifold of lower genus. The minimal value g of the splitting surface is...
smooth immersed minimalsurfaces. At the time it was known from Almgren–Pitts min-max theory the existence of at least one minimalsurface. Kei Irie, Fernando...
a Scherk surface (named after Heinrich Scherk) is an example of a minimalsurface. Scherk described two complete embedded minimalsurfaces in 1834; his...
on the choice of a direction on the surface or manifold. This leads to the concepts of maximal curvature, minimal curvature, and mean curvature. In Tractatus...
In visual arts, music and other media, minimalism is an art movement that began in post–World War II in Western art, most strongly with American visual...
catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimalsurface, meaning that it occupies...
cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimalsurface, specifically a minimalsurface of revolution. A hanging...
geometry. He is specially remembered for his work on the theory of minimalsurfaces. Raised in Bronx, he went to Bronx High School of Science (diploma...
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