标题： 关于海森堡可求长性中的密度问题 显示英文标题

标题： On the Density Problem in Heisenberg Rectifiability

摘要： 我们解决了Mattila、Serapioni和Serra Cassano提出的问题，关于密度假设在Heisenberg群中低余维可求长集表征中的作用。 具体而言，我们证明了正下密度条件是不需要的：可求长性完全由几乎处处存在近似切子群的几何性质决定。 这为子黎曼设置中的可求长集提供了一个简化且内在的准则，并加强了与Federer经典欧几里得定理的类比。 显示英文摘要

摘要： We resolve a problem posed by Mattila, Serapioni and Serra Cassano concerning the role of density assumptions in the characterization of rectifiable sets of low codimension in Heisenberg groups. Specifically, we prove that the positive lower density condition is not required: rectifiability is completely determined by the geometric property of almost everywhere existence of approximate tangent subgroups. This provides a simplified and intrinsic criterion for rectifiable sets in the subRiemannian setting and sharpens the analogy with Federer's classical Euclidean theorem.