A Frobenius–Nirenberg theorem with parameter
A Frobenius–Nirenberg theorem with parameter
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带参数的 Frobenius-Nirenberg 定理
DOI：
10.1515/crelle-2017-0051
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Xianghong Gong
中科院分区：
文献类型：
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作者：
Xianghong Gong
Newlander-Nirenberg定理指出，形式上可积的复结构与复欧氏空间中的复结构局部等价。我们将给出含参数Newlander-Nirenberg定理的两个结果。第一个将Newlander-Nirenberg定理推广到参数化的版本，它的证明产生了一个尖锐的正则性结果，就像韦伯斯特对Newlander-Nirenberg定理的证明一样。第二个版本涉及尼伦伯格的复杂弗罗贝纽斯定理和它的证明产生的结果与一个轻微的损失的规律性。
Abstract The Newlander–Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the complex structure in the complex Euclidean space. We will show two results about the Newlander–Nirenberg theorem with parameter. The first extends the Newlander–Nirenberg theorem to a parametric version, and its proof yields a sharp regularity result as Webster’s proof for the Newlander–Nirenberg theorem. The second concerns a version of Nirenberg’s complex Frobenius theorem and its proof yields a result with a mild loss of regularity.