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 new numerical method for the isometric embedding of 2-geometriesspecified by their 2-metrics in three dimensional Euclidean space. Our approachis to directly solve the fundamental embedding equation supplemented by sixconditions that fix translations and rotations of the embedded surface. Thisset of equations is discretized by means of a pseudospectral collocation pointmethod. The resulting nonlinear system of equations are then solved by aNewton-Raphson scheme. We explain our numerical algorithm in detail. Bystudying several examples we show that our method converges provided we startthe Newton-Raphson scheme from a suitable initial guess. Our novel method isvery efficient for smooth 2-metrics.

New efficient algorithm for the isometric embedding of 2-surface metrics in 3 dimensional Euclidean space