论文标题
关于抛物线空间中的密度问题
On the density problem in the parabolic space
论文作者
论文摘要
在这项工作中，我们扩展了许多经典结果，这些结果将密度，切线和重新讨论性之间的关系与抛物线空间之间的关系之间的关系，即配备了抛物线扩张的$ \ Mathbb {r}^{n+1} $。特别是，我们证明了一般维度度量的Marstand-Mattila重新讨论性标准，我们通过密度的内在整流措施提供了表征，并且我们研究了$ 1 $ sodimensixional均匀度量的结构。最后，我们将一些结果应用于对抛物线可重构性的定量版本的研究：我们证明，$ 1 $ $ primensitional ahlfors-regular-grounder量度的弱恒定密度条件意味着双侧弱的几何引理。
In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely $\mathbb{R}^{n+1}$ equipped with parabolic dilations. In particular we prove a Marstrand-Mattila rectifiability criterion for measures of general dimension, we provide a characterisation through densities of intrinsic rectifiable measures, and we study the structure of $1$-codimensional uniform measures. Finally, we apply some of our results to the study of a quantitative version of parabolic rectifiability: we prove that the weak constant density condition for a $1$-codimensional Ahlfors-regular measure implies the bilateral weak geometric lemma.
