An inequality relating volume, area and number of lattice points of convex sets in \(n\)-dimensional Euclidean space

DOI10.1007/BF01111393zbMath0238.52005MaRDI QIDQ2553089

Jürgen Bokowski, Hugo Hadwiger, Jörg M. Wills

Publication date: 1972

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/171781

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40)

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Cites Work

• Volumen und Oberfläche eines Eikörpers, der keine Gitterpunkte überdeckt
• Ein Satz über konvexe Körper und Gitterpunkte
• Volume, surface area and the number of integer points covered by a convex set
• Gitterperiodische Punktmengen und Isoperimetrie
• Eine Ungleichung zwischen Volumen, Oberfläche und Gitterpunktanzahl konvexer Mengen imR 3
• Évaluation de la différence entre l'aire d'une région plane convexe et le nombre des points aux coordonnées entières couverts par elle