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 study the exponential map of group of volume-preserving diffeomorphisms onclosed orientable surfaces via the vorticity formulation of the incompressibleEuler equation. We present an alternative, fluid dynamical proof of the theoremof Ebin--Misio\l{}ek--Preston: the exponential is a nonlinear Fredholm mappingof index zero. We extend Shnirelman's rigidity result for the exponential mapfrom 2-dimensional flat torus to arbitrary orientable closed surfaces. That is,we prove that the exponential map is Fredholm quasiregular.

On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity