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Length of a curve is quasi-convex along a teichm¨ uller geodesic

Anna Lenzhen Universite de Rennes Kasra Rafi University of Oklahoma

Differential Geometry mathscidoc:1609.10225

Journal of Differential Geometry, 88, (2), 267-295, 2011
We show that for every simple closed curve , the extremal length and the hyperbolic length of are quasi-convex functions along any Teichm¨uller geodesic. As a corollary, we conclude that, in Teichm¨uller space equipped with the Teichm¨uller metric, balls are quasi-convex.
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@inproceedings{anna2011length,
  title={LENGTH OF A CURVE IS QUASI-CONVEX ALONG A TEICHM¨ ULLER GEODESIC},
  author={Anna Lenzhen, and Kasra Rafi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913203951690817886},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={2},
  pages={267-295},
  year={2011},
}
Anna Lenzhen, and Kasra Rafi. LENGTH OF A CURVE IS QUASI-CONVEX ALONG A TEICHM¨ ULLER GEODESIC. 2011. Vol. 88. In Journal of Differential Geometry. pp.267-295. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913203951690817886.
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