Event

Yulan Qing, University of Toronto

Wednesday, January 24, 2018 14:45
Burnside Hall Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Convexity of balls in the outer space.

In this talk we answer questions regarding 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 α, the length of α along a balanced folding path is not larger than the maximum of its lengths at the end points. This implies that out-going balls are weakly convex. We then show that these results are sharp by providing several counterexamples.

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