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Minkowski's successive minima

by Henk, M., Wills, J.M..

Series: 2006-09, Preprints

11H06 Lattices and convex bodies
52C07 Lattices and convex bodies in $n$ dimensions

In this note we give a brief survey on some classical
and old problems involving Minkowski's successive minima of a
0-symmetric convex body as well as on some
recent developments concerning these functionals. Among others we show
that the successive minima are closely related to intrinsic
volumes, the lattice point enumerator, the zeros of the Ehrhart
polynomial and to simultaneous Diophantine approximation problems.

successive minima, convex bodies, lattices, Ehrhart polynomial