Self-gravitating cosmic strings and the Alexandrov’s inequality for Liouville-type equations
Self-gravitating cosmic strings and the Alexandrov’s inequality for Liouville-type equations
Motivated by the study of self-gravitating cosmic strings, we pursue the well-known method by Bandle to obtain a weak version of the classical Alexandrov’s isoperimetric inequality. In fact, we derive some quantitative estimates for weak subsolutions of a Liouville-type equation with conical singularities. Actually, we succeed in generalizing previously known …