MathDB

9

Part of 2008 IMS

Problems(1)

A map from interval to square

Source: IMS 2008

5/10/2008
Let γ:[0,1]→[0,1]×[0,1] \gamma: [0,1]\rightarrow [0,1]\times [0,1] be a mapping such that for each s,t∈[0,1] s,t\in [0,1] |\gamma(s) \minus{} \gamma(t)|\leq M|s \minus{} t|^\alpha in which α,M \alpha,M are fixed numbers. Prove that if γ \gamma is surjective, then α≤12 \alpha\leq\frac12
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