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 study time-like hypersurfaces with vanishing mean curvature in the (3+1)dimensional Minkowski space, which are the hyperbolic counterparts to minimalembeddings of Riemannian manifolds. The catenoid is a stationary solution ofthe associated Cauchy problem. This solution is linearly unstable, and we showthat this instability is the only obstruction to the global nonlinear stabilityof the catenoid. More precisely, we prove in a certain symmetry class theexistence, in the neighborhood of the catenoid initial data, of a co-dimension1 Lipschitz manifold transverse to the unstable mode consisting of initial datawhose solutions exist globally in time and converge asymptotically to thecatenoid.

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space