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Published June 2015 | public
Journal Article

Asymptoticity of grafting and Teichmüller rays II

Abstract

We show that any grafting ray in Teichmüller space is (strongly) asymptotic to some Teichmüller geodesic ray. Given a grafting ray, we define its limiting surface, and a conformally equivalent singular-flat surface of infinite area that represents the limit of the desired Teichmüller ray. The proof involves building quasiconformal maps of low dilatation between the surfaces along the rays. Our preceding work had proved the result for rays determined by an arational lamination or a multicurve, and the unified approach here gives an alternative proof of the former case.

Additional Information

© 2014 Springer Science+Business Media Dordrecht. Received: 11 June 2013; Accepted: 26 January 2014; Published online: 6 February 2014.

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023