# Gauss' theorem

## Gauss' theorem

[′gau̇s ‚thir·əm] (mathematics)

The assertion, under certain light restrictions, that the volume integral through a volume

*V*of 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 of*V*. 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.

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