Mahler-type theorem and non-collapsed limits of sub-Riemannian compact Heisenberg manifolds
Year: 2024
Type: article
Abstract: 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.
Source: Journal of Topology and Analysis
Author: Kenshiro Tashiro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403453692