Convergence results in Diophantine approximation on manifolds

描述：这个项目的目标是开发度量丢番图近似中获得上界的技术。这个广泛的主题涉及测量理论估计的特殊丢番图集和建立Khintchine和Jarnik型的结果。这个项目的具体目标将包括一个Hausdorff措施推广的Jarnik-Besicovitch定理多项式[1]和发展类似的理论一般子流形的欧氏空间以外的平面曲线和非齐次逼近。特别地，我们将寻求扩展Huang [2]和Beresnevich [3]的工作。Bernik，Hausdorff维数在丢番图逼近理论中的应用。（俄文）Acta Arith. 42（1983），第3期，219-253页。[2]J. - J. Huang，Hausdorff theory of dual approximation on planar curves，to appear in Crelle's Journal. [3]V. Beresnevich，A Groshev type theorem for convergence on manifold.匈牙利数学学报。94（2002），no. 1-2，99-130。

Description: The goal of this project to develop techniques for obtaining upper bounds in metric Diophantine approximation. This broad topic involves measure theoretic estimates for exceptional Diophantine sets and establishing Khintchine and Jarnik type results. The specific goals of this project will include a Hausdorff measure generalisation of the Jarnik-Besicovitch theorem for polynomials [1] and developing similar theory for generic submanifolds of a Euclidean space beyond planar curves and for inhomogeneous approximations. In particular, we will seek to extend the work of Huang [2] and Beresnevich [3].References:[1] V. I. Bernik, Application of the Hausdorff dimension in the theory of Diophantine approximations. (Russian) Acta Arith. 42 (1983), no. 3, 219-253. [2] J.-J. Huang, Hausdorff theory of dual approximation on planar curves, to appear in Crelle's Journal. [3] V. Beresnevich, A Groshev type theorem for convergence on manifolds. Acta Math. Hungar. 94 (2002), no. 1-2, 99-130.