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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The aim of the paper is to prove the following result concerning moduli ofcurve families in the Heisenberg group. Let $\Omega$ be a domain in theHeisenberg group foliated by a family $\Gamma$ of legendrian curves. Assumethat there is a quadratic differential $q$ on $\Omega$ in the kernel of anoperator defined in \cite{Tim2} and every curve in $\Gamma$ is a horizontaltrajectory for $q$. Let $l_\Gamma : \Omega \rightarrow ]0,+\infty[$ be thefunction that associates to a point $p\in \Omega$, the $q$-length of the leafcontaining $p$. Then, the modulus of $\Gamma$ is \[ M_4 (\Gamma) = \int_\Omega\frac{|q|^2}{(l_\Gamma) ^4} \mathrm{d} L^3.\]

Moduli of Legendrian foliations and quadratic differentials in the Heisenberg group