Federer Measures, Good and Nonplanar Functions of Metric Diophantine Approximation

Abstract

The goal of this paper is to generalize the main results of [1] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish “joint strong extremality” of arbitrary finite collection of smooth nondegenerate submani- folds of .The proof was based on quantitative nondivergence estimates for quasi-polynomial flows on the space of lattices.