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

Polyharmonic, or $r$-harmonic, maps are a natural generalization of harmonicmaps whose study was proposed by Eells-Lemaire in 1983. The main aim of thispaper is to construct new examples of proper $r$-harmonic immersions intospheres. In particular, we shall prove that the canonical inclusion $i:S^{n-1}(R)\to S^n$ is a proper $r$-harmonic submanifold of $S^n$ if and only ifthe radius $R$ is equal to $1/ \sqrt{r}$. We shall also prove the existence ofproper $r$-harmonic generalized Clifford's tori into the sphere.

New examples of r-harmonic immersions into the sphere