Friendly measures, homogeneous flows and singular vectors
Dmitry Kleinbock, Barak Weiss
Abstract
We prove that singular vectors have measure zero with respect to any friendly measure on Rn (e.g. the volume measure on a nondegenerate submanifold). This generalizes special cases considered by Davenport-Schmidt, Baker and Bugeaud. The main tool is quantitative nondivergence estimates for quasi-polynomial flows on homogeneous spaces.
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