A star body (with respect to the origin 0) in ℝ
≧ 3) which has 0 as center of symmetry is uniquely determined by the (
− 1)-dimensional volumes of its sections with hyperplanes through 0. Without the symmetry assumption, we show that a star body is uniquely determined by the volumes and centroids of its hyperplane sections through 0. For convex bodies, we prove a stability version of this result.
Gardner, R. J.
, Encyclopedia of Mathematics and its Applications, vol. 58. Cambridge University Press, Cambridge 1995.
Gardner R. J., '', in Geometric Tomography, (1995) -.
Gardner R. J.Geometric Tomography1995)| false
and Weil, W.
, Average section functions for star-shaped sets,
Adv. Appl. Math.
(2006), no. 1, 70–84.
Weil W., 'Average section functions for star-shaped sets' (2006) 36Adv. Appl. Math.: 70-84.
Weil W.Average section functions for star-shaped setsAdv. Appl. Math.2006367084)| false