In
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
, the Neovius surface is a
triply periodic minimal surface
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 ...
originally discovered by Finnish mathematician Edvard Rudolf Neovius (the uncle of
Rolf Nevanlinna
Rolf Herman Nevanlinna (né Neovius; 22 October 1895 – 28 May 1980) was a Finnish mathematician who made significant contributions to complex analysis.
Background
Nevanlinna was born Rolf Herman Neovius, becoming Nevanlinna in 1906 when his fat ...
).
The surface has
genus
Genus ( plural genera ) is a taxonomic rank used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In the hierarchy of biological classification, genus com ...
9, dividing space into two infinite non-equivalent labyrinths. Like many other triply periodic minimal surfaces it has been studied in relation to the microstructure of
block copolymers
In polymer chemistry, a copolymer is a polymer derived from more than one species of monomer. The polymerization of monomers into copolymers is called copolymerization. Copolymers obtained from the copolymerization of two monomer species are some ...
,
surfactant
Surfactants are chemical compounds that decrease the surface tension between two liquids, between a gas and a liquid, or interfacial tension between a liquid and a solid. Surfactants may act as detergents, wetting agents, emulsifiers, foaming ...
-water mixtures, and crystallography of soft materials.
It can be approximated with the
level set
In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is:
: L_c(f) = \left\~,
When the number of independent variables is two, a level set is calle ...
surface
:
In
Schoen's categorisation it is called the C(P) surface, since it is the "complement" of the
Schwarz P surface. It can be extended with further handles, converging towards the expanded regular octahedron (in Schoen's categorisation)
[Ken Brakke, C-P Family of Triply Periodic Minimal Surfaces, http://www.susqu.edu/brakke/evolver/examples/periodic/cpfamily.html]
References
{{Minimal surfaces
Differential geometry
Minimal surfaces