Minimality in asymmetry classes

• Autorzy: Michał Wiernowolski
• Języki publikacji: EN

Abstrakty

EN

We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].

Słowa kluczowe

EN

convex sets; symmetry; minimality; Hausdorff metric

Kategorie tematyczne

• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 2
• Strony: 149-154

Daty

wydano

1997

otrzymano

1996-05-23

poprawiono

1996-12-12

Twórcy

autor

Michał Wiernowolski

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Bibliografia

• [1] J. Grzybowski, Minimal pairs of convex compact sets, Arch. Math. (Basel) 63 (1994), 173-181.
• [2] D. Pallaschke, S. Scholtes and R. Urbański, On minimal pairs of convex compact sets, Bull. Polish Acad. Sci. Math. 39 (1991), 1-5.
• [3] R. Schneider, On asymmetry classes of convex bodies, Mathematika 21 (1974), 12-18.
• [4] G. C. Shephard and G. Ewald, Normed vector spaces consisting of classes of convex sets, Math. Z. 91 (1966), 1-19.
• [5] R. Urbański, A generalization of the Minkowski-Rådström-Hörmander Theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 709-715.