ScalingStacks

Lemma 2.9 . [0406]

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Lemma 2.9.

The holomorphic functions z0,z1,z2z_{0},z_{1},z_{2} extend smoothly over 𝔇i⊂𝔇⊂ℝμ1,μ22×ℂη\mathfrak{D}_{i}\subset\mathfrak{D}\subset\mathbb{R}^{2}_{\mu_{1},\mu_{2}}\times\mathbb{C}_{\eta}. The function z0,z1,z2z_{0},z_{1},z_{2} vanish over 𝔇1∪𝔇2\mathfrak{D}_{1}\cup\mathfrak{D}_{2}, 𝔇1∪𝔇3\mathfrak{D}_{1}\cup\mathfrak{D}_{3} and 𝔇2∪𝔇3\mathfrak{D}_{2}\cup\mathfrak{D}_{3} respectively.

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