Gauss' theorem

Gauss' theorem [′gau̇s ‚thir·əm]

(mathematics)

The assertion, under certain light restrictions, that the volume integral through a volumeVof the divergence of a vector function is equal to the surface integral of the exterior normal component of the vector function over the boundary surface ofV. Also known as divergence theorem; Green's theorem in space; Ostrogradski's theorem.

At a point on a surface the product of the principal curvatures is an invariant of the surface, called the Gaussian curvature.