Extremal subspaces and their submanifolds
Number Theory
2007-05-23 v2 Dynamical Systems
Abstract
It is known that the properties of almost all points of R^n being not very well (multiplicatively) approximable are inherited by nondegenerate in R^n (read: not contained in a proper affine subspace) smooth submanifolds. In this paper we consider submanifolds which are contained in proper affine subspaces, and prove that the aforementioned diophantine properties pass from a subspace to its nondegenerate submanifold. The proofs are based on a correspondence between multidimensional diophantine approximation and dynamics of lattices in Euclidean spaces.
Cite
@article{arxiv.math/0210367,
title = {Extremal subspaces and their submanifolds},
author = {Dmitry Kleinbock},
journal= {arXiv preprint arXiv:math/0210367},
year = {2007}
}
Comments
26 pages. To appear in Geom. Funct. Anal. Several misprints corrected