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 prove a number of results on the number of solutions to the asymptoticPlateau problem in $\mathbb H^3$. In the direction of non-uniqueness, weconstruct an example of a quasicircle that is the asymptotic boundary ofuncountably many pairwise distinct stable minimal disks.  Moreover, we discuss criteria that ensure uniqueness. Given a Jordan curve$\Lambda$ in the asymptotic boundary of $\mathbb H^3$, we show that uniquenessof the minimal surfaces with asymptotic boundary $\Lambda$ is equivalent touniqueness in the smaller class of stable minimal disks, and, when $\Lambda$ isinvariant by a Kleinian group, to uniqueness in the even smaller class of groupinvariant stable minimal disks.  Finally, we show that if a quasicircle (or more generally, a Jordan curve offinite width) $\Lambda$ is the asymptotic boundary of a minimal surface$\Sigma$ with principal curvatures less than or equal to 1 in absolute value,then uniqueness holds.

Uniqueness and non-uniqueness for the asymptotic Plateau problem in hyperbolic space