Dual Diophantine Approximation on Planar Curves: General Hausdorff theory
AuthorBlane, Michael Anthony
Mathematics and Statistics
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The general Hausdorff theory of Dual Diophantine approximation on manifolds was initiated by the work of Beresnevich, Dickinson, and Velani, in which they established that the set of ψ -approximable points on a manifold has full measure when a certain sum diverges. A decade later, Hussain established the convergence counterpart to the above result in the case of the parabola. Not long after, Huang proved a convergence result for all planar curves with regards to the Hausdorff s-measure. In this thesis, we extend Huang's convergence result to the Hausdorff g-measure for all planar curves.