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

We establish a nonlinear analogue of a splitting map into a Euclidean space,as a harmonic map into a flat torus. We prove that the existence of such a mapimplies Gromov-Hausdorff closeness to a flat torus in any dimension.Furthermore, Gromov-Hausdorff closeness to a flat torus and an integral boundon the scalar curvature imply the existence of a harmonic splitting map.Combining these results with Stern's inequality, we provide a newGromov-Hausdorff stability theorem for flat $3$-tori. The main tools we employinclude the harmonic map heat flow, Ricci flow, and both Ricci limits and RCDtheories.

Gromov-Hausdorff stability of tori under Ricci and integral scalar curvature bounds