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 that any weakly acausal curve   Γ   in the boundary of anti‐de Sitter (2+1)‐space is the asymptotic boundary of two spacelike   K  ‐surfaces, one of which is past‐convex and the other future‐convex, for every    K  ∈  (  −  ∞  ,  −  1  )   . The curve   Γ   is the graph of a quasisymmetric homeomorphism of the circle if and only if the   K  ‐surfaces have bounded principal curvatures. Moreover in this case a uniqueness result holds.  The proofs rely on a well‐known correspondence between spacelike surfaces in anti‐de Sitter space and area‐preserving diffeomorphisms of the hyperbolic plane. In fact, an important ingredient is a representation formula, which reconstructs a spacelike surface from the associated area‐preserving diffeomorphism.  Using this correspondence we then deduce that, for any fixed    θ  ∈  (  0  ,  π  )   , every quasisymmetric homeomorphism of the circle admits a unique extension which is a   θ  ‐landslide of the hyperbolic plane. These extensions are quasiconformal.

Area‐preserving diffeomorphisms of the hyperbolic plane and K ‐surfaces in anti‐de Sitter space