Covering a reduced polygon by a disk

• Autorzy: Fabińska E.
• Języki publikacji: EN

Abstrakty

EN

A convex body R in Euclidean d-space Ed is reduced if every convex body K C R different from R has thickness smaller than the thickness A(R) of R. We prove that every reduced polygon P C E2 is contained in a disk of radius A(P) centered at a boundary point of P.

Słowa kluczowe

EN

reduced convex body; reduced polygon; width

PL

bryła wypukła; wielobok

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 4
• Strony: 851--855
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Fabińska E.

• University of Technology Kaliskiego 7, 85-796 Bydgoszcz, Poland,

Bibliografia

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• [2] B. V. Dekster, On reduced convex bodies, Israel J. Math. 56 (1986), 247-256.
• [3] E. Fabińska, M. Lassak, Reduced bodies in normed planes, Israel J. Math. 161 (2007), 75-87.
• [4] H. Groemer, Extremal convex sets, Monatsh. Math. 96 (1983), 29-39.
• [5] M. Lassak, Reduced convex bodies in the plane, Israel J. Math. 70 (1990), 365-379.
• [6] M. Lassak, On the smallest disk containing a planar reduced convex body, Arch. Math. 80 (2003), 553-560.
• [7] M. Lassak, H. Martini, Reduced bodies in Minkowski space, Acta Math. Hungar. 106 (2005), 17-26.
• [8] H. Martini, K. J. Swanepoel, Non-planar simplices are not reduced, Publ. Math. Debrecen 64 (2004), 101-106.