On common summands and anti-summands of compact convex sets

• Autorzy: Grzybowski J. , Urbański A. , Wiernowolski M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we examine families of common summands and anti-summands of compact convex sets. In particular, we prove the equivalence of minimality problems for common anti-summands and minimal pairs of compact convex sets. We also give partial answers to the question whether minimal anti-summands of polytopes are polytopes as well.

Słowa kluczowe

EN

minimal pairs of compact convex sets; Minkowski sum; summand

PL

geometria dyskretna; pary minimalne; suma Minkowskiego; zbiór wypukły zwarty

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 1
• Strony: 69--76
• Opis fizyczny: Bibliogr. 7 poz.,

Twórcy

autor

Grzybowski J.

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

autor

Urbański A.

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

autor

Wiernowolski M.

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

Bibliografia

• [1] J. Grzybowski, A note on summands of compact convex sets, Mathematika, 43 (1996) 286-299.
• [2] J. Grzybowski, Minimal pairs of convex compact sets, Arch. Math., 63 (1994) 173-181.
• [3] D. Pallaschke, S. Scholtes, R. Urbański, On minimal pairs of convex compact sets, Bull. Pol. Ac.: Math., 39 (1991) 105--109.
• [4] D. Pallaschke, W. Urbańska, R. Urbański, C-minimal pairs of compact convex sets, Journal of Convex Anal., 4 (1997) 1-25.
• [5] D. Pallaschke, R. Urbański, A continuum of minimal pairs of compact convex sets which are not connected by translations, Journal of Convex Anal., 3 (1996) 83-95.
• [6] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, in: Encyclopedia of Math. and its Appl., Vol. 44, Cambridge University Press, Cambridge 1993.
• [7] S. Schaltes, Minimal pairs of convex bodies in two dimensions, Mathematika, 39 (1992) 267-273.