  We derive the isoperimetric profile of Gaussian type for an absolutely
continuous probability measure on Euclidean spaces with respect to the Lebesgue
measure, whose density is a radial function.The key is a generalization of the
Poincar\'e limit which asserts that the $n$-dimensional Gaussian measure is
approximated by the projections of the uniform probability measure on the
Euclidean sphere of appropriate radius to the first $n$-coordinates as the
dimension diverges to infinity. The generalization is done by replacing the
projections with certain maps.
