Bobkov, S. G. Isoperimetric and analytic inequalities for log-concave probability measures. (English) Zbl 0964.60013 Ann. Probab. 27, No. 4, 1903-1921 (1999). It is shown that the probability measures on Euclidean space with logarithmically concave densities have positive isoperimetric constants in the sense of Cheeger and thus always share Poincaré-type inequalities. Then those log-concave measures are described which satisfy inequalities of Gaussian type. Reviewer: S.Ebralidze (Tbilisi) Cited in 4 ReviewsCited in 89 Documents MSC: 60E15 Inequalities; stochastic orderings 46G12 Measures and integration on abstract linear spaces Keywords:logarithmically concave measures; isoperimetric inequalities; Poincaré-type inequalities PDFBibTeX XMLCite \textit{S. G. Bobkov}, Ann. Probab. 27, No. 4, 1903--1921 (1999; Zbl 0964.60013) Full Text: DOI