Extremal subspaces and their submanifolds |
| |
Authors: | D Kleinbock |
| |
Institution: | (1) Department of Mathematics, Brandeis University,Waltham, MA 02454-9110, USA.E-mail: kleinboc@brandeis.edu, US |
| |
Abstract: | It was proved in the paper KM1] that the properties of almost all
points of being not very well (multiplicatively) approximable are
inherited by nondegenerate in (read: not contained in a proper
affine subspace) smooth submanifolds. In this paper we consider submanifolds
which are contained in proper a.ne 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.
Submitted: March 2002; Revision: August 2002 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|