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

We present a numerical method for solving Weyl's embedding problem whichconsists of finding a global isometric embedding of a positively curved andpositive-definite spherical 2-metric into the Euclidean three space. The methodis based on a construction introduced by Weingarten and was used in Nirenberg'sproof of Weyl's conjecture. The target embedding results as the endpoint of anembedding flow in R^3 beginning at the unit sphere's embedding. We employspectral methods to handle functions on the surface and to solve various(non)-linear elliptic PDEs. Possible applications in 3+1 numerical relativityrange from quasi-local mass and momentum measures to coarse-graining ininhomogeneous cosmological models.

Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity