Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev center

2005/09/13 by P. N. Ivanshin, Ivanshin, P. N., E. N. Sosov +1
Mathematics · #53C70 #54E40 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C70 #msc:54E40

paper · pdf · doi:10.48550/arxiv.math/0509275

12 pages

arxiv created 2007/11/28 · arxiv updated 2009/12/01

Abstract

We prove local Lipschitz property of the map which puts in correspondence to each N--net different from (N-1)--net its Chebyshev center. If dimension of Eucledean or Lobachevskii space is greater than 1 and net consists of more than 2 points we show that this map is not Lipschits in a neighbourhood of the space of 2--nets embedded into the space of all N--nets endowed by Hausdorff metric.

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