Convexity of balls in outer space

  • Yulan Qing

    Fudan University, Shanghai, China
  • Kasra Rafi

    University of Toronto, Canada
Convexity of balls in outer space cover
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In this paper we study the convexity properties of geodesics and balls in Outer space equipped with the Lipschitz metric. We introduce a class of geodesics called balanced folding paths and show that, for every loop , the length of along a balanced folding path is not larger than the maximum of its lengths at the endpoints. This implies that out-going balls are weakly convex. We then show that these results are sharp by providing several counter examples.

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Yulan Qing, Kasra Rafi, Convexity of balls in outer space. Groups Geom. Dyn. 15 (2021), no. 3, pp. 893–934

DOI 10.4171/GGD/615