Extremal subspaces and their submanifolds

Details Extremal subspaces and their submanifolds Extremal subspaces and their submanifolds

2002-10-23

arxiv.org/abs/math/0210367v2

GAFA 13 (2003), 437-466

Mathematics

Number Theory

26 pages. To appear in Geom. Funct. Anal. Several misprints corrected

Scientific paper

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.

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