Critical lattices, elliptic curves and their possible dynamics

Abstract

We present a combinatorial geometry and dynamical systems framework for the investigation and proof of the Minkowski conjecture about critical determinant of the region $|x{|}^p+|y{|}^p<1,p>1.$ The application of the framework may drastically reduce the investigation of sufficiently smooth real functions of many variables. Incidentally, we establish connections between critical lattices, dynamical systems and elliptic curves.

7 pages, Latex