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

Motivated by the study of self gravitating cosmic strings, we pursue the wellknown method by C. Bandle to obtain a weak version of the classicalAlexandrov's isoperimetric inequality. In fact we derive some quantitativeestimates for weak subsolutions of a Liouville-type equation with conicalsingularities. Actually we succeed in generalizing previously known results,including Bol's inequality and pointwise estimates, to the case where thesolutions solve the equation just in the sense of distributions. Next, wederive some \uv{new} pointwise estimates suitable to be applied to a class ofsingular cosmic string equations. Finally, interestingly enough, we apply theseresults to establish a minimal mass property for solutions of the cosmic stringequation which are \uv{supersolutions} of the singular Liouville-type equation.

Self gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations