Curves as measured foliation on noncompact surfaces
type: Item
instance of: scholarly article
title: Curves as measured foliation on noncompact surfaces
zbMATH Open document ID: 0803.57004
DOI: 10.1007/BF02843943
author: A. Portolano
author: Ignazia Maniscalco
publication date: 1995-01-05T00:00:00Z
review text: Let \(M\) be a noncompact orientable surface, and let \(c\) be a simple closed curve which is not homotopic to a disk or to a boundary component. The authors prove that there exists a measured foliation \((F_ c, \mu)\) on \(M\) with the property that \(c\) is a leaf of \(F_ c\), and for every homotopy class \(\alpha\) of simple closed curves on \(M\), we have \(I ((F_ c, \mu), \alpha)= i(c, \alpha)\), where \(I((F_ c, \mu), \alpha)\) is as usual the least upper bound of the set of total mass of curves in the class \(\alpha\) with respect to the measure \(\mu\), and \(i(c,\alpha)\) is the minimum of the number of intersection points with \(c\) of curves in the class \(\alpha\). The result, in the case of compact surfaces, in part of Thurston's theory, and the ingredient which the authors use for the noncompact case is the classification of noncompact surfaces.
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 490571
zbMATH Keywords: two-dimensional manifold
zbMATH Keywords: noncompact orientable surface
zbMATH Keywords: measured foliation
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 490571