page_title: Mean curvature
section_title: Minimal surfaces
hierarchical_section_title: Mean curvature / Minimal surfaces
caption_attribution_description: en:Costa_minimal_surface
context_page_description: In mathematics, the mean curvature of a surface is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space.
  The concept was used by Sophie Germain in her work on elasticity theory. Jean Baptiste Marie 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 the analysis of physical interfaces between fluids which, for example, have constant mean curvature in static flows, by the Young-Laplace equation.
context_section_description: A minimal surface is a surface which has zero mean curvature at all points. Classic examples include the catenoid, helicoid and Enneper surface. Recent discoveries include Costa's minimal surface and the Gyroid.
caption: A rendering of Costa's minimal surface.
exif: {}