Isoperimetric regions in the hyperbolic plane between parallel horocycles
The reviewed paper is devoted to the classical isoperimetric problem in the hyperbolic plane. Let \(\mathcal F\) be the region inside two parallel horocycles of \(\mathbb R^2_+\), represented by two horizontal Euclidean straight lines. The author considers the following problem: Fix an area value and study the domains \(\Omega\subset\mathcal F\) with the prescribed area which have minimal free boundary perimeter, but not counting its part of the boundary contained in the horocycles. He gives a detailed and complete classification of the isoperimetric solutions through isoperimetric inequalities.
scientific article; zbMATH DE number 6116571
scientific article