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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider the mean curvature rigidity problem of an equatorial zone on asphere which is symmetric about the equator with width $2w$. There are twodifferent notions on rigidity, i.e. strong rigidity and local rigidity. Weprove that for each kind of these rigidity problems, there exists a criticalvalue such that the rigidity holds true if, and only if, the zone width issmaller than that value. For the rigidity part, we used the tangency principleand a specific lemma (the trap-slice lemma we established before). For thenon-rigidity part, we construct the nontrivial perturbations by a gluingprocedure called the round-corner lemma using the Delaunay surfaces.

Can One Perturb the Equatorial Zone on a Sphere with Larger Mean Curvature?