Abstract
We present new expressions for the integrals of mean curvature of domains in Rn by means of sections with cylinders. Then, we combine these expressions with the corresponding version of the invariant density of affine subspaces in Rn, in order to obtain pseudo-rotational formulae for all the integrals of mean curvature of ∂K. As particular cases, we present pseudo-rotational integral formulas for the volume, area, integral of mean curvature, and Euler-Poincaré characteristic of a connected domain of R3, whose boundary is a surface, considering slabs in R3 whose central plane passes through a fixed point, and cylinders contained in these slabs.
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