06-09
Minkowski's successive minima
Preprint series: 06-09, Preprints
- MSC:
- 11H06 Lattices and convex bodies, See also {11P21, 52C05, 52C07}
- 52C07 Lattices and convex bodies in $n$ dimensions, See Also {11H06, 11H31, 11P21}
Abstract: 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.
Keywords: successive minima, convex bodies, lattices, Ehrhart polynomial
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.