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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Displaying similar documents to “On isoperimetric inequalities in Minkowski spaces.”
Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.
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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.
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Journal of Inequalities and Applications [electronic only]
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On Busemann surface area of the unit ball in Minkowski spaces.
Mustafaev, Zokhrab (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Hyperplane sections of convex bodies in isotropic position.
Fradelizi, Matthieu (1999)
Beiträge zur Algebra und Geometrie
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On the Busemann-Petty Problem for Perturbations of the Ball.
J. Bourgain (1991)
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Approximation of convex bodies by sums of line segments
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Portugaliae mathematica
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Permanence of moment estimates for p-products of convex bodies
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.
Spherical and ellipsoidality theorems for convex bodies
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Portugaliae mathematica
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Eric L. Grinberg (1991)
Mathematische Annalen
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The skeleta of convex bodies
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.
Fixing and hindering systems in combinatorial geometry.
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Beiträge zur Algebra und Geometrie
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