In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below)...

In differential geometry, the Schwarz minimal surfaces are periodic minimal surfaces originally described by Hermann Schwarz. In the 1880s Schwarz and...

In mathematics, Costa's minimal surface or Costa's surface, is an embedded minimal surface discovered in 1982 by the Brazilian mathematician Celso José...

In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in R 3 {\displaystyle \mathbb {R} ^{3}} that is invariant under...

In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose...

list of surfaces in mathematics. They are divided into minimal surfaces, ruled surfaces, non-orientable surfaces, quadrics, pseudospherical surfaces, algebraic...

\end{aligned}}} It was introduced by Alfred Enneper in 1864 in connection with minimal surface theory. The Weierstrass–Enneper parameterization is very simple, f...

periodic minimal surface discovered by Alan Schoen in 1970. It arises naturally in polymer science and biology, as an interface with high surface area. The...

Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published in 1867. Surfaces in the...

In mathematics, Bour's minimal surface is a two-dimensional minimal surface, embedded with self-crossings into three-dimensional Euclidean space. It is...

although many more have been discovered. Minimal surfaces can also be defined by properties to do with surface area, with the consequence that they provide...

developable surface or be folded flat; the flattened Möbius strips include the trihexaflexagon. The Sudanese Möbius strip is a minimal surface in a hypersphere...

proved that every simply-connected minimal surface in 3-dimensional Euclidean space is isometric to a Bryant surface by a holomorphic parameterization...

produces this minimal surface of revolution. There are only two minimal surfaces of revolution (surfaces of revolution which are also minimal surfaces): the plane...

Meusnier used it in 1776, in his studies of minimal surfaces. It is important in the analysis of minimal surfaces, which have mean curvature zero, and in...

rotated and lifted along its fixed axis of rotation. It is the third minimal surface to be known, after the plane and the catenoid. It was described by...

molecules results in a minimal surface area. As a result of surface area minimization, a surface will assume a smooth shape. Surface tension, represented...

area of a minimal surface decreases as the manifold undergoes Ricci flow. Perelman verified what happened to the area of the minimal surface when the manifold...

a Scherk surface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834; his...

combinatorics. His notable contributions included discovering a periodic minimal surface in the space R 3 {\displaystyle \mathbb {R} ^{3}} ; stating the famous...

Minimal surfaces of class VII (those with no rational curves with self-intersection −1) are called surfaces of class VII0. Every class VII surface is...

capillary surfaces with gravity absent have constant mean curvature, so that a minimal surface is a special case of static capillary surface. They are...

Costa's minimal surface Catenoid Enneper surface Gyroid Helicoid Lidinoid Riemann's minimal surface Saddle tower Scherk surface Schwarz minimal surface Triply...

surface of degree 15 Bour's minimal surface, a surface of degree 16 Richmond surfaces, a family of minimal surfaces of variable degree Coble surfaces...

mathematical problem of minimal surface. They will assume the shape of least surface area possible containing a given volume. A true minimal surface is more properly...

Plateau examined soap films, leading him to formulate the concept of a minimal surface. The German biologist and artist Ernst Haeckel painted hundreds of...

geometry, constant-mean-curvature (CMC) surfaces are surfaces with constant mean curvature. This includes minimal surfaces as a subset, but typically they are...

Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function is linear? This is true for...

connected by Plateau borders. Soap films can be used as model systems for minimal surfaces, which are widely used in mathematics. Daily experience[citation needed]...

catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies...