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 construct free boundary minimal disc stackings, with any number of strata,in the three-dimensional Euclidean unit ball, and prove uniform, linear lowerand upper bounds on the Morse index of all such surfaces. Among other things,our work implies for any positive integer $k$ the existence of $k$-tuples ofdistinct, pairwise non-congruent, embedded free boundary minimal surfaces allhaving the same topological type. In addition, since we prove that theequivariant Morse index of any such free boundary minimal stacking, withrespect to its maximal symmetry group, is bounded from below by (the integerpart of) half the number of layers and from above strictly by twice the samenumber, it follows that any possible realization of such surfaces via anequivariant min-max method would need to employ sweepouts with an arbitrarilylarge number of parameters. This also shows that it is only for $N=2$ and $N=3$layers that free boundary minimal disc stackings are achievable by means ofone-dimensional mountain pass schemes.

Disc stackings and their Morse index