Displaying similar documents to “Convex bodies with circumscribing boxes of constant volume”

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

Paul Goodey (2009)

Banach Center Publications

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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

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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.

A general geometric construction for affine surface area

Elisabeth Werner (1999)

Studia Mathematica

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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 → 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 ≥ 0 , B t t ≥ 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].