Displaying similar documents to “Generalization Of An Inequality Of G. Pólya Concerning The Eigenfrequences Of Vibrating Bodies”

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...

On Hadwiger's problem on inner parallel bodies

Eugenia Saorín (2009)

Banach Center Publications

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We consider the problem of classifying the convex bodies in the 3-dimensional space depending on the differentiability of their associated quermassintegrals with respect to the one-parameter-depending family given by the inner/outer parallel bodies. It turns out that this problem is closely related to some behavior of the roots of the 3-dimensional Steiner polynomial.

Minkowski valuations intertwining the special linear group

Christoph Haberl (2012)

Journal of the European Mathematical Society

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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.

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.