mean curvature in a sentence

Examples

1. The term " k "-noid and trinoid is also sometimes used for constant mean curvature surfaces, especially branched versions of the unduloid ( " triunduloids " ).
2. By the Young Laplace equation the curvature of a soap film is proportional to the difference in pressure between the sides : if it is zero, the membrane has zero mean curvature.
3. The fact that mean curvature represents the rate of change in area follows from applying the above equation to F \ equiv 1 since \ int _ S \, dS is area:
4. The surface is designated trapped if the cross sections of both congruences decrease in area as they exit the surface; and this is apparent in the mean curvature vector, which is:
5. In normal topology hexagonal phases, which are formed by type I amphiphiles, the hydrocarbon chains are contained within the cylindrical aggregates such that the polar-apolar interface has a positive mean curvature.
6. For manifolds embedded in a K�hler Einstein manifold, if the surface is a Lagrangian submanifold, the mean curvature flow is of Lagrangian type, so the surface evolves within the class of Lagrangian submanifolds.
7. :A different choice is the mean curvature, which for a sphere " will be " the reciprocal of its radius .-- T 15 : 04, 15 May 2006 ( UTC)
8. Capillary pressure is a function of the mean curvature of the interface at a given location at the surface, meaning the pressure is dependent on the two radii of curvature that give the shape of the surface.
9. One further work of Germain's on elasticity was published posthumously in 1831 : her " M�moire sur la courbure des surfaces . " She used the mean curvature in her research ( see Honors in Number Theory ).
10. The " Germain curvature " ( also called mean curvature ) is \ frac { k _ 1 + k _ 2 } { 2 }, when and are the maximum and minimum values of the normal curvature.