The Brunn-Minkowski inequality in spaces with bitriangular laws of composition

被引：0

作者：

Bobkov S.G. ^{[1
]}

机构：

[1] University of Minnesota, Minneapolis, MN 55455

来源：

Journal of Mathematical Sciences | 2011年 / 179卷 / 1期

关键词：

Convex Body; Heisenberg Group; Isoperimetric Inequality; Minkowski Inequality; Isoperimetric Problem;

D O I：

10.1007/s10958-011-0580-7

中图分类号：

学科分类号：

摘要：

The Brunn-Minkowski inequality and Prékopa-Leindler's theorem are considered with respect to bitriangular laws of composition on Euclidean spaces Rn. The result is illustrated by an example of the Heisenberg group Hn. Bibliography: 11 titles. © 2011 Springer Science+Business Media, Inc.

引用

页码：2 / 6

页数：4

共 11 条

[1]

Burago Y.D., Zalgaller V.A., Geometric Inequalities, (1988)

[2]

Monti R., Brunn-Minkowski and isoperimetric inequality in the Heisenberg group, Ann. Acad. Sci. Fenn. Math., 28, 1, pp. 99-109, (2003)

[3]

Leonardi G.P., Masnou S., On the isoperimetric problem in the Heisenberg group H<sup>n</sup>, Ann. Mat. Pura Appl. (4), 184, 4, pp. 533-553, (2005)

[4]

Knothe H., Contributions to the theory of convex bodies, Michigan Math. J., 4, pp. 39-52, (1957)

[5]

Bobkov S.G., Large deviations via transference plans, Adv. Math. Res., 2, pp. 151-175, (2003)

[6]

Bobkov S.G., Large deviations and isoperimetry over convex probability measures with heavy tails, Electron. J. Probab., 12, pp. 1072-1100, (2007)

[7]

Prekopa A., Logarithmic concave measures with applications to stochastic programming, Acta Sci. Math. (Szeged), 32, pp. 301-316, (1971)

[8]

Prekopa A., On logarithmic concave measures and functions, Acta Sci. Math. (Szeged), 34, pp. 335-343, (1973)

[9]

Leindler L., On a certain converse of Hölder's inequality. II, Acta Sci. Math. (Szeged), 33, 3-4, pp. 217-223, (1972)

[10]

Pisier G., The Volume of Convex Bodies and Banach Space Geometry, (1989)

← 1 2 →