Characterization of Gaussian measures by the isoperimetric property of half-spaces

If the half-spaces of the form {x∈Rⁿ:x₁≤c} are extremal in the isoperimetric problem for a product-measure μⁿ, n≥2, then the marginal distribution of μ is Gaussian. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 31–38.