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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we first provide precise tensorial formulae for the asymptoticoperators of contact instantons $w:\dot \Sigma \to Q$ and of pseudoholomorphiccurves $u:(\dot\Sigma,j) \to (Q \times \mathbb R, \widetilde J)$ on thesymplectization of contact manifold $(Q,\lambda)$. The formula exhibitsexplicit dependence on the compatible pair $(\lambda,J)$ of the given contacttriad $(Q,\lambda, J)$. Then based on this, we present a perturbation theory ofthe asymptotic operator under the change of compatible CR almost complexstructure $J$ for given contact form $\lambda$. This perturbation theory hasbeen missing in the literature on the study of pseudoholomorphic curves onsymplectization. Through this systematic tensorial approach, we also providethe study of finer asymptotic behavior at the punctures, such as convergence oftangent plane of contact instantons, in terms of the eigenvalues andeigenvectors of the asymptotic operator, which also simplifies thecorresponding study of pseudoholomorphic curves on symplectization in theliterature.

Perturbation theory of asymptotic operators of contact instantons and pseudoholomorphic curves on symplectization