English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study a non-collapsed Gromov--Hausdorff limit of a sequenceof compact Heisenberg manifolds with sub-Riemannian metrics. In the case ofstrictly sub-Riemannian case, we show that if a sequence has an upper bound ofthe diameter and a lower bound of Popp's measure, then it has a convergentsubsequence in the Gromov--Hausdorff topology, and the limit is isometric to acompact Heisenberg manifold of the same dimension. The same conclusion is alsoshown for Riemannian case with the additional assumption on Ricci curvaturelower bounds.

Mahler type theorem and non-collapsed limits of sub-Riemannian compact Heisenberg manifolds