Abstract
We prove inequalities relating the inradius of a convex body with interior containing no point of the integral lattice, with the volume or surface area of the body. These inequalities are tight and generalize previous results.
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The work of the second author was supported by the Gerhard-Hess-Forschungs-Förderpreis of the German Science Foundation (DFG) awarded to Günter M. Ziegler (Zi 475/1-1)
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Awyong, P.W., Henk, M. & Scott, P.R. Note on lattice-point-free convex bodies. Monatshefte für Mathematik 126, 7–12 (1998). https://doi.org/10.1007/BF01312452
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DOI: https://doi.org/10.1007/BF01312452