Mahler’s work on the geometry of numbers
Jan-Hendrik EvertseUniversiteit Leiden, Mathematisch Instituut, Postbus 9512, 2300 RA Leiden, The Netherlands
Mahler has written many papers on the geometry of numbers. Arguably, his most influential achievements in this area are his compactness theorem for lattices, his work on star bodies and their critical lattices, and his estimates for the successive minima of reciprocal convex bodies and compound convex bodies. We give a, by far not complete, overview of Mahler's work on these topics and their impact.