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

The purposes of the present paper are two-fold. Firstly we further developthe interplay between the contact Hamiltonian geometry and the geometricanalysis of Hamiltonian-perturbed contact instantons with the Legendrianboundary condition, which is initiated by the present author in\cite{oh:contacton-Legendrian-bdy}. We introduce the class of \emph{tamecontact manifolds} $(M,\lambda)$, which includes compact ones but notnecessarily compact, and establish uniform a priori $C^0$-estimates for thecontact instantons. Then we study the problem of estimating the Reeb-untanglingenergy of one Legendrian submanifold from another, and formulate a particularlydesigned parameterized moduli space for the study of the problem. We establishthe Gromov-Floer-Hofer type convergence result for contact instantons of finiteenergy and construct its compactification of the moduli space, first bydefining the correct energy and then by proving uniform a priori energy boundsin terms of the oscillation of the relevant contact Hamiltonian. Secondly, asan application of this geometry and analysis of contact instantons, we provethat the \emph{self Reeb-untangling energy} of a compact Legendrian submanifold$R$ in any tame contact manifold $(M,\lambda)$ is greater than that of theperiod gap $T_\lambda(M,R)$ of the Reeb chords of $R$. This is an optimalresult in general.In a sequel \cite{oh:shelukhin-conjecture}, we also proveShelukhin's conjecture specializing to the Legendrianization ofcontactomorphisms and utilizing its $\mathbb Z_2$-symmetry argument as thefixed point set of anti-contact involution.

Geometry and analysis of contact instantons and entanglement of Legendrian links I