ScalingStacks

Proposition [03PZ]

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Proposition

If we choose z0∈Bj0z_{0}\in B_{j_{0}} so that

(uj0,δ−u)​(z0)=χ⁡(δ)​δα,(u_{j_{0},\delta}-u)(z_{0})=\chi(\delta)\delta^{\alpha},

then

supM∖E(uδ−v)<(uδ−v)​(z0).\sup_{M\setminus E}(u_{\delta}-v)<(u_{\delta}-v)(z_{0}).

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