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 construct an explicit example of a smooth isotopy $\{\xi_t\}_{t \in[0,1]}$ of volume- and orientation-preserving diffeomorphisms on $[0,1]^n$ ($n\geq 3$) that has infinite total kinetic energy. This isotopy has noself-cancellation and is supported on countably many disjoint tubularneighbourhoods of homothetic copies of the isometrically embedded image of$(M,g)$, a "topologically complicated" Riemannian manifold-with-boundary.However, there exists another smooth isotopy that coincides with $\{\xi_t\}$ at$t=0$ and $t=1$ but of finite total kinetic energy.

A smooth isotopy of volume-preserving diffeomorphisms on unit cube saving energy through extra dimensions