Quantitative isoperimetric inequalities for log-convex probability measures on the line
نویسندگان
چکیده
منابع مشابه
On Isoperimetric Inequalities for Log-convex Measures
Let μ = ρdx be a Borel measure on Rd. A Borel set A ⊂ R is a solution of the isoperimetric problem if for any B ⊂ R satisfying μ(A) = μ(B) one has μ(∂A) ≤ μ(∂B), where μ(∂A) = ∫ ∂A ρ dHd−1 is the corresponding surface measure. There exists only a small number of examples where the isoperimetric problem has an exact solution. The most important case is given by Lebesgue measure λ on R, the solut...
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Received July 1995; revised April 1996. 1Research supported in part by ISF Grant NXZ000 and NXZ300 and by the Alexander von Humboldt-Stiftung. This author enjoyed the hospitality of the Faculty of Wiskunde and Informatica, Free University of Amsterdam and of the Faculty of Mathematics, Bielefeld University, while part of this research was carried out. 2Research supported in part by an NSF Postd...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2014.05.005