The topology of surface mediatrices
type: Item
instance of: scholarly article
title: The topology of surface mediatrices
zbMATH Open document ID: 1141.57008
author: James Bernhard
author: J. J. P. Veerman
published in: Topology and its Applications
publication date: 2006-12-14T00:00:00Z
full work available at URL: https://pdxscholar.library.pdx.edu/mth_fac/130
review text: Given two points of a metric space the mediatrix is the set of all points which have the same distance from both points. In the paper under review the authors examine the topological structure of mediatrices in connected, compact 2-manifolds with respect to the metric induced from a Riemannian metric. Building on previous work [Topology Appl. 153, No. 9, 1421--1433 (2006; Zbl 1093.54007)] they show that all such mediatrices are homeomorphic to a finite simplicial \(1\)-complex. Furthermore, they determine all five possible complexes for the torus and conjecture the set of possible homeomorphism classes of mediatrices for surfaces of higher genus.
reviewed by: Nils Rosehr
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 5080154
zbMATH Keywords: minimally separating sets
zbMATH Keywords: geodesics
zbMATH Keywords: compact surfaces
zbMATH Keywords: simplicial complexes
MaRDI profile type: Publication
OpenAlex ID: W1986260643
cites work: Simplicial Structure of the Real Analytic Cut Locus
cites work: Q4003026
cites work: Q5538378
cites work: Q4023819
cites work: Minimally separating sets, mediatrices, and Brillouin spaces
DOI: 10.1016/J.TOPOL.2006.03.016
description: scientific article; zbMATH DE number 5080154