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

Isoperimetric profile of radial probability measures on Euclidean spaces