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

We present a proof of a conjecture proposed by V. Delecroix, E. Goujard, P.Zograf, and A. Zorich, which describes the large genus asymptotic behaviours ofthe ratio of frequencies of separating over nonseparating simple closedgeodesics on a closed hyperbolic surface of genus $g$ with $n$ cusps. Weexplicitly give the function $f(\frac{n}{g})$ in the conjecture. The moderatebehaviour of the frequencies with respect to the growth rate of the number ofcusps compared to that of the genus drastically contrasts with the behaviour ofother geometric quantities and exhibits the topological nature of thefrequencies.

Mirzakhani's frequencies of simple closed geodesics on hyperbolic surfaces in large genus and with many cusps