论文标题
Mahler型定理和亚里曼尼亚副型海森贝格歧管的非限制
Mahler type theorem and non-collapsed limits of sub-Riemannian compact Heisenberg manifolds
论文作者
论文摘要
在本文中，我们研究了一系列带有亚riemannian指标的紧凑型海森伯格歧管的非collaps gromov- hausdorff极限。在严格的亚riemannian情况下，我们表明，如果一个序列具有直径的上限和POPP度量的下限，那么它在gromov-hausdorff拓扑中具有收敛的子序列，并且极限对于相同高层的紧凑型高伯格属均具有等值。对于Riemannian情况，还显示了同样的结论，以及RICCI曲率下限的其他假设。
In this paper, we study a non-collapsed Gromov--Hausdorff limit of a sequence of compact Heisenberg manifolds with sub-Riemannian metrics. In the case of strictly sub-Riemannian case, we show that if a sequence has an upper bound of the diameter and a lower bound of Popp's measure, then it has a convergent subsequence in the Gromov--Hausdorff topology, and the limit is isometric to a compact Heisenberg manifold of the same dimension. The same conclusion is also shown for Riemannian case with the additional assumption on Ricci curvature lower bounds.
