ScalingStacks

Lemma 4.12 . [0240]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Lemma 4.12.

For |x1|+|x2|≫1|x_{1}|+|x_{2}|\gg 1, the local Ck,αC^{k,\alpha}-norm of the metric gluing error

‖η⁡(C~​x2x1)​(ϕD1(2)−u)‖k,α,l​o​c=O⁡(x1−2​n−1n−1).\left\lVert\eta(\tilde{C}\frac{x_{2}}{x_{1}})(\phi_{D_{1}}^{(2)}-u)\right\rVert_{k,\alpha,loc}=O(x_{1}^{-\frac{2n-1}{n-1}}).

In particular the glued metric remains Kähler.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.