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

In this paper, we give an equivariant compactification of the space PFlat(S)of homothety classes of half-translation structures on a compact, connected,orientable surface S. We introduce the space PMix(S) of homothety classes ofmixed structures on S, that are CAT(0) tree-graded spaces in the sense of Drutuand Sapir, with pieces which are R-trees and completions of surfaces endowedwith half-translation structures. Endowing Mix(S) with the equivariant Gromovtopology, and using asymptotic cone techniques, we prove that PMix(S) is anequivariant compactification of PFlat(S), thus allowing us to understand in ageometric way the degenerations of half-translation structures on S. We finallycompare our compactification to the one of Duchin-Leininger-Rafi, based ongeodesic currents on S, by the mean of the translation distances of theelements of the covering group of S.

Geometric compactification of moduli spaces of half-translation structures on surfaces