Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.

Mustafaev, Zokhrab

Displaying similar documents to “Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.”

On Busemann surface area of the unit ball in Minkowski spaces.

Mustafaev, Zokhrab (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Similarity:

On isoperimetric inequalities in Minkowski spaces.

Martini, Horst, Mustafaev, Zokhrab (2010)

Journal of Inequalities and Applications [electronic only]

Similarity:

Approximation of convex bodies by sums of line segments

Lindquist, Norman F. (1975)

Portugaliae mathematica

Similarity:

On a question of Milman and Alesker concerning the monotonicity of a domain functional.

Keady, Grant (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Similarity:

Some new Brunn-Minkowski-type inequalities in convex bodies.

Zhao, Chang-Jian, Leng, Gangsong, Debnath, Lokenath (2005)

International Journal of Mathematics and Mathematical Sciences

Similarity:

A measure of asymmetry for convex surfaces

Asplund, E., Bredon, G., Grünbaum, B. (1960)

Portugaliae mathematica

Similarity:

Around the Rogers-Shepard inequality.

Böröczky, Károly jun. (1996)

Mathematica Pannonica

Similarity:

The skeleta of convex bodies

David G. Larman (2009)

Banach Center Publications

Similarity:

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.

The mean surface area of the boxes circumscribed about a convex body

Rolf Schneider (1972)

Annales Polonici Mathematici

Similarity:

Spherical and ellipsoidality theorems for convex bodies

Dorn, C. (1978)

Portugaliae mathematica

Similarity:

A general geometric construction for affine surface area

Elisabeth Werner (1999)

Studia Mathematica

Similarity:

Let K be a convex body in $ℝ^{n}$ and B be the Euclidean unit ball in $ℝ^{n}$ . We show that $l i m_{t \to 0} (| K | - | K_{t} |) / (| B | - | B_{t} |) = a s (K) / a s (B)$ , where as(K) respectively as(B) is the affine surface area of K respectively B and ${K_{t}}_{t \geq 0}$ , ${B_{t}}_{t \geq 0}$ are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].

One functional-analytical idea by Alexandrov in convex geometry.

Kutateladze, S.S. (2002)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

Similarity:

Support functions of central convex bodies

Lindquist, Norman F. (1975)

Portugaliae mathematica

Similarity:

A measure of axial symmetry of centrally symmetric convex bodies

Marek Lassak, Monika Nowicka (2010)

Colloquium Mathematicae

Similarity:

Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for...