A Dini-type condition suffices for Hölder curve coverage in quasiconvex metric spaces, implying upper box dimension d allows α-Hölder curves for α < 1/d, with a counterexample for α = 1/d in the plane.
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Box-counting by H\"older's traveling salesman
A Dini-type condition suffices for Hölder curve coverage in quasiconvex metric spaces, implying upper box dimension d allows α-Hölder curves for α < 1/d, with a counterexample for α = 1/d in the plane.