论文标题
固定的简单和连接到抛物面的套件的产品
Pinned simplices and connections to product of sets on paraboloids
论文作者
论文摘要
在本文中，我们获得了对应于抛物面的紧凑子集的点产物集的提高尺寸阈值。作为这些估计值的直接应用，我们获得了最知名的维度阈值的重大改进，这些阈值确保了给定的欧几里得空间的紧凑子集决定了所有可能的单纯形式的所有可能一致性类别的正比例。在许多制度中，这改善了先前由Erdogan-Hart-Iosevich（\ cite {ehi}），greenleaf-iosevich-liu-palsson（\ cite {gilp}）等获得的结果。
In this paper we obtain improved dimensional thresholds for dot product sets corresponding to compact subsets of a paraboloid. As a direct application of these estimates, we obtain significant improvements to the best known dimensional thresholds that guarantee that a given compact subset of Euclidean space determines a positive proportion of all possible congruence classes of simplexes. In many regimes this improves the results previously obtained by Erdogan-Hart-Iosevich (\cite{EHI}), Greenleaf-Iosevich-Liu-Palsson (\cite{GILP}) and others.
