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- W2897623575 abstract "As part of his celebrated Complex Frobenius Theorem, Nirenberg showed that given a smooth elliptic structure (on a smooth manifold), the manifold is locally diffeomorphic to an open subset of $mathbb{R}^rtimes mathbb{C}^n$ (for some $r$ and $n$) in such a way that the structure is locally the span of $frac{partial}{partial t_1},ldots, frac{partial}{partial t_r},frac{partial}{partial overline{z}_1},ldots, frac{partial}{partial overline{z}_n}$; where $mathbb{R}^rtimes mathbb{C}^n$ has coordinates $(t_1,ldots, t_r, z_1,ldots, z_n)$. In this paper, we give optimal regularity for the coordinate charts which achieve this realization. Namely, if the manifold has Zygmund regularity of order $s+2$ and the structure has Zygmund regularity of order $s+1$ (for some $s>0$), then the coordinate chart may be taken to have Zygmund regularity of order $s+2$. We do this by generalizing Malgrange's proof of the Newlander-Nirenberg Theorem to this setting." @default.
- W2897623575 created "2018-10-26" @default.
- W2897623575 creator A5077939778 @default.
- W2897623575 date "2018-10-23" @default.
- W2897623575 modified "2023-09-27" @default.
- W2897623575 title "Sharp Regularity for the Integrability of Elliptic Structures" @default.
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- W2897623575 hasPublicationYear "2018" @default.
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