Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.
Mustafaev, Zokhrab (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Mustafaev, Zokhrab (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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L. Lovász, R. Kannan, M. Simonovits (1995)
Discrete & computational geometry
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Zhao, Chang-Jian, Leng, Gangsong, Debnath, Lokenath (2005)
International Journal of Mathematics and Mathematical Sciences
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Horst Martini, Zokhrab Mustafaev (2012)
Colloquium Mathematicae
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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.
Lin, Si, Bin, Xiong, Wuyang, Yu (2006)
Journal of Inequalities and Applications [electronic only]
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Mustafaev, Zokhrab (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Fradelizi, Matthieu (1999)
Beiträge zur Algebra und Geometrie
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J. Bourgain (1991)
Geometric and functional analysis
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Lindquist, Norman F. (1975)
Portugaliae mathematica
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Ulrich Brehm, Hendrik Vogt, Jürgen Voigt (2002)
Studia Mathematica
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It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies in ℝⁿ are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the Γ-function.
Dorn, C. (1978)
Portugaliae mathematica
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Eric L. Grinberg (1991)
Mathematische Annalen
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David G. Larman (2009)
Banach Center Publications
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The connectivity and measure theoretic properties of the skeleta of convex bodies in Euclidean space are discussed, together with some long standing problems and recent results.
Boltyanski, V., Martini, H. (1999)
Beiträge zur Algebra und Geometrie
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