ON UNIT BALLS AND ISOPERIMETRICES IN NORMED SPACES

被引：6

作者：

Martini, Horst ^{[1
]}

Mustafaev, Zokhrab ^{[2
]}

机构：

[1] Univ Technol Chemnitz, Fac Math, D-09107 Chemnitz, Germany

[2] Univ Houston Clear Lake City, Dept Math, Houston, TX 77058 USA

来源：

COLLOQUIUM MATHEMATICUM | 2012年 / 127卷 / 01期

关键词：

Busemann volume; cross-section measures; ellipsoids; Holmes-Thompson volume; inner radius; intersection body; isoperimetrix; Minkowski space; outer radius; projection body; INEQUALITY; AREA;

D O I：

10.4064/cm127-1-10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.

引用

页码：133 / 142

页数：10

共 18 条

[1] On the inequality for volume and Minkowskian thickness [J].

Averkov, Gennadiy .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2006, 49 (02) :185-195

[2]

Busemann H., 1956, Math. Scand, V4, P88, DOI [10.7146/math.scand.a-10457, DOI 10.7146/MATH.SCAND.A-10457]

[3]

Gardner R. J., 2006, ENCY MATH APPL, V58

[4] N-DIMENSIONAL AREA AND CONTENT IN MINKOWSKI SPACES [J].

HOLMES, RD ;

THOMPSON, AC .

PACIFIC JOURNAL OF MATHEMATICS, 1979, 85 (01) :77-110

[5]

Koldobsky A., 2005, FOURIER ANAL CONVEX, V116

[6] Approximation of convex bodies by centrally symmetric bodies [J].

Lassak, M .

GEOMETRIAE DEDICATA, 1998, 72 (01) :63-68

[7]

Lutwak E., 1993, Handbook of Convex Geometry, P151, DOI [10.1016/B978-0-444-89596-7.50010-9, DOI 10.1016/B978-0-444-89596-7.50010-9]

[8]

Martini H., 2006, AEQUATIONES MATH, V72, P110, DOI DOI 10.1007/s00010-006-2825-y

[9]

Martini H., 1994, C MATH SOC J BOLYAI, V63, P269

[10]

Martini H., 2006, Period. Math. Hungar, V53, P185, DOI [10.1007/s10998-006-0031-2, DOI 10.1007/S10998-006-0031-2]

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