We prove that the mappings obtained in Forstnerič splitting lemma vary in a \(\mathcal {C}^{\lfloor {\frac{l-1}{2}}\rfloor }\)-continuous way if only the input family of biholomorphic mappings close to Id (and their domains) is \(\mathcal {C}^l\)-continuous (see Theorem 1.3 for a precise formulation).

中文翻译：

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光滑依赖参数的双亚纯映象的分解引理

我们证明在Forstnerič分裂引理中获得的映射以\（\ mathcal {C} ^ {\ lfloor {\ frac {l-1} {2}} \ rfloor} \）连续变化，如果仅输入族接近Id（及其域）的双全纯映射是\（\ mathcal {C} ^ l \） -连续的（精确定理请参见定理1.3）。