Convex polygons and the isoperimetric problem in simply connected space forms $M_{\kappa }^2$

A R Aithal, Anisa M H Chorwadwala

In this article, we prove that there exists a unique perimeter minimizer among all piecewise smooth simple closed curves in $M_{\kappa }^2$ enclosing area $A>0$ $(A\le 2\pi$ if $\kappa =1)$,…