Moduli of rotundity and smoothness for convex bodies.
Clemente Zanco, Adele Zucchi (1990)
Extracta Mathematicae
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Clemente Zanco, Adele Zucchi (1990)
Extracta Mathematicae
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Lassak, Marek (2008)
Beiträge zur Algebra und Geometrie
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J. Bourgain (1991)
Geometric and functional analysis
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Jentsch, Lothar, Natroshvili, David (1999)
Memoirs on Differential Equations and Mathematical Physics
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Horváth, Á.G. (2009)
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Keith Ball (1991)
Inventiones mathematicae
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Gardner, R.J., Koldobsky, A., Schlumprecht, T. (1999)
Annals of Mathematics. Second Series
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Victor Klee, Libor Veselý, Clemente Zanco (1996)
Studia Mathematica
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For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation...
Zhang, Gaoyong (1999)
Annals of Mathematics. Second Series
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Lassak, Marek, Nowicka, Monika (2009)
Beiträge zur Algebra und Geometrie
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V. Klee, P. Gritzmann (1992)
Discrete & computational geometry
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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...
Dorn, C. (1978)
Portugaliae mathematica
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