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arXiv · 1403.8038

Hausdorff theory of dual approximation on planar curves

Jing-Jing Huang
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Abstract

Ten years ago, Beresnevich-Dickinson-Velani initiated a project that develops the general Hausdorff measure theory of dual approximation on non-degenerate manifolds. In particular, they established the divergence part of the theory based on their general ubiquity framework. However, the convergence counterpart of the project remains wide open and represents a major challenging question in the subject. Until recently, it was not even known for any single non-degenerate manifold. In this paper, we settle this problem for all curves in $\mathbb{R}^2$, which represents the first complete theory of its kind for a general class of manifolds.

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Jing-Jing Huang. 2014-03-31. Hausdorff theory of dual approximation on planar curves. https://arxiv.org/abs/1403.8038

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