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

Authors
  • Bartolucci, Daniele
  • Castorina, Daniele
Type
Preprint
Publication Date
Sep 10, 2014
Submission Date
Sep 10, 2014
Identifiers
arXiv ID: 1409.3135
Source
arXiv
License
Yellow
External links

Abstract

Motivated by the study of self gravitating cosmic strings, we pursue the well known method by C. 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 results, including Bol's inequality and pointwise estimates, to the case where the solutions solve the equation just in the sense of distributions. Next, we derive some \uv{new} pointwise estimates suitable to be applied to a class of singular cosmic string equations. Finally, interestingly enough, we apply these results to establish a minimal mass property for solutions of the cosmic string equation which are \uv{supersolutions} of the singular Liouville-type equation.

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