ScalingStacks

Lemma 4.10 . [00RR]

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Lemma 4.10.

Let Φ\Phi be a psh function on the {|zi|≤4,∀i}⊂ℂn\{|z_{i}|\leq 4,\forall i\}\subset\mathbb{C}^{n}. Then

−∫B1|Φ|≲−∫{1<|zi|<4,∀i}|Φ|.\mathchoice{{\vbox{\hbox{$\textstyle-$ }}\kern-7.98003pt}}{{\vbox{\hbox{$\scriptstyle-$ }}\kern-6.26338pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.6363pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.45924pt}}\!\int_{B_{1}}|\Phi|\lesssim\mathchoice{{\vbox{\hbox{$\textstyle-$ }}\kern-7.98003pt}}{{\vbox{\hbox{$\scriptstyle-$ }}\kern-6.26338pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.6363pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.45924pt}}\!\int_{\{1<|z_{i}|<4,\forall i\}}|\Phi|.

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