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

This is the first of a series of papers in preparation in which we study theHamiltonian perturbed contact instantons with Legendrian boundary condition andits applications. In this paper, we prove that the asymptotic charge of contactinstantons at the punctures under the Legendrian boundary condition vanishes,which eliminates the phenomenon of the appearance of `spiraling cusp instantonalong a Reeb core'. This removes the only remaining obstacle towards thecompactification and the Fredholm theory of the moduli space of contactinstantons in the open string case, which plagues the closed string case. Wealso extend the a priori elliptic coercive estimates for the contact instantonswith boundary, and prove an asymptotic exponential $C^\infty$-convergenceresult at a puncture under the uniform $C^1$ bound. In a sequel to the presentpaper, we study the $C^1$ estimates by defining a proper notion of energy forthe contact instantons, and develop a Fredholm theory and construct aGromov-type compactification of the moduli space of contact instantons withLegendrian boundary condition and of finite energy, and apply them to problemsin contact topology and dynamics.

Contact Hamiltonian dynamics and perturbed contact instantons with Legendrian boundary condition