论文标题
与亚riemannian指标的紧凑型海森堡流形的崩溃限制
Collapsed limits of compact Heisenberg manifolds with sub-Riemannian metrics
论文作者
论文摘要
在本文中，我们表明，紧凑的海森堡歧管的每个崩溃的gromov-hausdorff极限都是平坦的圆环。在这里，我们说，如果次 - 黎曼歧管的一系列序列相对于POPP的体积或最小POPP的体积收敛到零，则会崩溃。在附录中，我们给出了亚riemannian heisenberg歧管上的收缩不平等，并观察到总测量的指数等于Hausdorff维度的倒数。
In this paper, we show that every collapsed Gromov--Hausdorff limit of compact Heisenberg manifolds is isometric to a flat torus. Here we say that a sequence of sub-Riemannian manifolds collapses if their total measure with respect to the Popp's volume or the minimal Popp's volume converges to zero. In the appendix, we give the systolic inequality on sub-Riemannian Heisenberg manifolds, and observe that the exponent of the total measure is equal to the inverse of the Hausdorff dimension.
