ISSN:
1436-5081
Keywords:
52A20
;
52A22
;
star bodies
;
spherical integral transformations
;
convex bodies
;
stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetK be ad-dimensional star body (with respect to the origino). It is known that the (d−1)-dimensional volume of the intersections ofK with the hyperplanes througho does not uniquely determineK. Uniqueness can only be achieved under additional assumptions, such as central symmetry. Here it is pointed out that if one uses, instead of intersections by hyperplanes, intersections by half-planes that containo on the boundary, then, without any additional assumptions, the volume of these intersections determinesK uniquely. This assertion, and more general results of this kind, together with stability estimates, are obtained from uniqueness results and estimates concerning a particular spherical integral transformation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01473582
