Time-Varying Vector Fields and Their Flows by Saber Jafarpour & Andrew D. Lewis

Author:Saber Jafarpour & Andrew D. Lewis
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

for suitable , with r = kn. From the proof of Theorem 3.8 we also have

and this gives the result.

To prove that the weak -topology is weaker than the COlip-topology, it suffices to show that is continuous for every if and are given the CO m+lip-topology. Thus let be compact and let . We choose a relatively compact geodesically convex chart about x ∈ K and compute, for distinct ,

for some , using the mean value theorem [1, Proposition 2.4.8], and where γ is the unique length minimising geodesic from x 2 to x 1. Thus we have an inequality

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