The horoboundary and isometry group of Thurston's Lipschitz metric - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: We show that the horofunction boundary of Teichm\-uller space with Thurston-sLipschitz metric is the same as the Thurston boundary. We use this to determinethe isometry group of the Lipschitz metric, apart from in some exceptionalcases. We also show that the Teichm\-uller spaces of different surfaces, whenendowed with this metric, are not isometric, again with some possibleexceptions of low genus.



Author: Cormac Walsh

Source: https://arxiv.org/



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