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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let RV1 be the (n+l)-dimensional Minkowski space, that is, Rn+l with the Lorentz metric < ,)―(dx1)2+ ・・・+(dxn)2―(dxn+1)z. It has been known that in R +1 hyperplanes are the only complete space-like hypersurfaces whose mean curvatures are zero. This Bernstein type theorem was proposed by Calabi, and solved by him [3] (for n^4) and by Cheng and Yau [5] (for all n) (see alsoIshihara [10] or Nishikawa [14]). On the other hand, for complete space-like hypersurfaces of nonzero constant mean curvature in Rnx+\ there are many nonlinear examples constructed by Treibergs [18], Hano and Nomizu [7], Isbihara and Hara [11] and others. In his recent paper, Palmer [17] discussed the Gauss map of a complete space-like hypersurface of constant mean curvature in 1??+1 and showed a condition for the hypersurface to be a hyperplane. This is a result analogous to the one obtained by Hoffman, Osserman and Schoen [9], who proved that the normals to a complete surface of constant mean curvature in the 3-dimensional Euclidean space Es cannot lie in a closed hemisphere of S*, unless the surface is a plane or a right circular cylinder. Note that a right circular cylinder is the simplest example of a complete non-umbilical surface of constant mean curvature in Es. In R"+1 the simplest example of a complete non-umbilical space-like hypersurface of constant mean curvature is given by the following:

On the Gauss map of complete space-like hypersurfaces of constant mean curvature in Minkowski space