Isoperimetric regions in the hyperbolic plane between parallel horocycles
type: Item
instance of: scholarly article
title: Isoperimetric regions in the hyperbolic plane between parallel horocycles
zbMATH Open document ID: 1266.53038
author: Márcio Fabiano da Silva
published in: Missouri Journal of Mathematical Sciences
publication date: 2012-12-18T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.mjms/1352138558
review text: 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.
reviewed by: Marian Hotloś
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53A35
zbMATH DE Number: 6116571
zbMATH Keywords: isoperimetric problem
zbMATH Keywords: hyperbolic plane
zbMATH Keywords: horocycle
zbMATH Keywords: geodesic halfdisk
zbMATH Keywords: horocycle halfdisk
MaRDI profile type: Publication
cites work: Isoperimetric curves on hyperbolic surfaces
cites work: A variational problem for constant mean curvature surfaces with free boundary.
cites work: A free boundary isoperimetric problem in hyperbolic 3-space between parallel horospheres
cites work: Screw motion surfaces in \(\mathbb H^2 \times \mathbb R\) and \(\mathbb S^2\times \mathbb R\)
cites work: The Isoperimetric Problem on Surfaces
cites work: Clusters minimizing area plus length of singular curves
cites work: Q3598569
cites work: Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems
cites work: THE ISOPERIMETRIC PROBLEM ON EUCLIDEAN, SPHERICAL, AND HYPERBOLIC SURFACES
cites work: Stability of a Liquid Drop Trapped Between Two Parallel Planes
description: scientific article; zbMATH DE number 6116571