Displaying similar documents to “Hyperplane sections of convex bodies in isotropic position.”

The determination of convex bodies from the size and shape of their projections and sections

Paul Goodey (2009)

Banach Center Publications

Similarity:

We survey results concerning the extent to which information about a convex body's projections or sections determine that body. We will see that, if the body is known to be centrally symmetric, then it is determined by the size of its projections. However, without the symmetry condition, knowledge of the average shape of projections or sections often determines the body. Rather surprisingly, the dimension of the projections or sections plays a key role and exceptional cases do occur...

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.

Permanence of moment estimates for p-products of convex bodies

Ulrich Brehm, Hendrik Vogt, Jürgen Voigt (2002)

Studia Mathematica

Similarity:

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.

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...

Minkowski valuations intertwining the special linear group

Christoph Haberl (2012)

Journal of the European Mathematical Society

Similarity:

All continuous Minkowski valuations which are compatible with the special linear group are completely classified. One consequence of these classifications is a new characterization of the projection body operator.