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/

Zendy Plus

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

Zendy Tools

Zendy Open

Flat surfaces that correspond to $k$-differentials on compact Riemannsurfaces are of finite area provided there is no pole of order $k$ or higher.We denote by \textit{flat surfaces with poles of higher order} those surfaceswith flat structures defined by a $k$-differential with at least one pole oforder at least $k$. Flat surfaces with poles of higher order have differentgeometrical and dynamical properties than usual flat surfaces of finite area.In particular, they can have a finite number of saddle connections. We givelower and upper bounds for the number of saddle connections and relatedquantities. In the case $k=1\ or\ 2$, we provide a combinatorialcharacterization of the strata for which there can be an infinite number ofsaddle connections.

Counting saddle connections in flat surfaces with poles of higher order