Extremal subspaces and their submanifolds

Extremal subspaces and their submanifolds
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极值子空间及其子流形

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发表时间：
2002
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通讯作者：
D. Kleinbock
D. Kleinbock
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作者：
D. Kleinbock

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抽象。在文献[KM 1]中证明了几乎所有 $ \mathbb{R}^{n} $的点不是很好（乘法）逼近的， 由$ \mathbb{R}^{n} $中的非退化继承（读作：不包含在适当的 仿射子空间）光滑子流形。本文考虑子流形 包含在适当的a.ne子空间中，并证明 上述丢番图性质是从一个子空间 到它的非退化子流形证明是基于一个对应关系 多维丢番图近似与 欧几里得空间中的格动力学。
Abstract. It was proved in the paper [KM1] that the properties of almost all points of $ \mathbb{R}^{n} $ being not very well (multiplicatively) approximable are inherited by nondegenerate in $ \mathbb{R}^{n} $ (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.