Yuqing Zhang
Multiplicative Diophantine Exponents of Hyperplanes and their Nondegenerate Submanifolds
Preprint series: ESI preprints

MSC:

22D40 Ergodic theory on groups, See also {28Dxx, 43A60}

28D99 None of the above, but in this section

58F11 Ergodic theory; invariant measures, See also {28Dxx}

11J13 Simultaneous homogeneous approximation, linear forms

Abstract: We consider multiparameter dynamics on the space of
unimolular lattices. Along with quantitative
nondivergence we prove that multiplicative Diophantine
exponents of hyperplanes are inherited by their
nondegenerate submanifolds.