For a given centred convex body K of R^n, let H(K) be the class of all convex bodies with the same projection body as K. The question whether K can be expressed as a Blaschke average of two non-homothetic bodies from H(K) is considered. Necessary and sufficient conditions on K to be Blaschke decomposable in H(K) are given. The paper provides also a characterization of the bodies K such that the Blaschke indecomposable bodies in H(K) are dense in H(K) itself.
Campi, S., Colesanti, A., Gronchi, P. (1998). Blaschke-decomposable convex bodies. ISRAEL JOURNAL OF MATHEMATICS, 105, 185-195 [10.1007/BF02780328].
Blaschke-decomposable convex bodies
CAMPI S.;
1998-01-01
Abstract
For a given centred convex body K of R^n, let H(K) be the class of all convex bodies with the same projection body as K. The question whether K can be expressed as a Blaschke average of two non-homothetic bodies from H(K) is considered. Necessary and sufficient conditions on K to be Blaschke decomposable in H(K) are given. The paper provides also a characterization of the bodies K such that the Blaschke indecomposable bodies in H(K) are dense in H(K) itself.
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https://hdl.handle.net/11365/22006
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