Schnell, U.; Wills, J. M. Two isoperimetric inequalities with lattice constraints. (English) Zbl 0737.52008 Monatsh. Math. 112, No. 3, 227-233 (1991). Two isoperimetric inequalities with lattice constraints for arbitrary lattices in the euclidean plane are proved. We generalize previous results by J. Bokowski, H. Hadwiger, and the second author [Math. Z. 127, 363-364 (1972; Zbl 0238.52005)] for the integer lattice \(\mathbb{Z}^ d\) (but all dimensions \(d\)) to general lattices. For arbitrary \(d\) a partial result is given. Reviewer: U.Schnell and J.M.Wills Cited in 8 Documents MSC: 52C05 Lattices and convex bodies in \(2\) dimensions (aspects of discrete geometry) 52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) 52A40 Inequalities and extremum problems involving convexity in convex geometry Keywords:lattice points; isoperimetric inequalities Citations:Zbl 0238.52005 PDFBibTeX XMLCite \textit{U. Schnell} and \textit{J. M. Wills}, Monatsh. Math. 112, No. 3, 227--233 (1991; Zbl 0737.52008) Full Text: DOI EuDML References: [1] Bokowski, J., Hadwiger, H., Wills, J. M.: Eine Ungleichung zwischen Volumen, Oberfläche und Gitterpunktanzahl konvexer Körper imn-dimensionalen Raum. Math. Z.127, 363-364 (1972). · Zbl 0238.52005 · doi:10.1007/BF01111393 [2] Gruber, P. M., Lekkerkerker, C. G.: Geometry of Numbers. Amsterdam: North Holland. 1987. · Zbl 0611.10017 [3] Hadwiger, H.: Gitterperiodische Punktmengen und Isoperimetrie. Mh. Math.76, 410-418 (1972). · Zbl 0248.52012 · doi:10.1007/BF01297304 [4] Wills, J. M.: Kugellagerungen und Konvexgeometrie. Jahresber. d. DMV92, 21-46 (1990). · Zbl 0688.52004 [5] Wills, J. M.: Bounds for the lattice point enumerator, in press. · Zbl 0738.52018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.