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

• Autorzy: Paul Goodey
• Języki publikacji: EN

Abstrakty

EN

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 but appear to be sporadic. In a rather different direction, we will see that combining information about the size of projections or sections with other information such as Steiner points or centres of gravity also leads to complete determination of the original body.

Kategorie tematyczne

• 52A22: Random convex sets and integral geometry
• 52A38: Length, area, volume
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 84
• Numer: 1
• Strony: 13-30

Daty

wydano

2009

Twórcy

autor

Paul Goodey

• Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA

Identyfikatory

DOI

10.4064/bc84-0-1