对数-Lipschitz子丛的Frobenius定理
The Frobenius Theorem for Log-Lipschitz Subbundles
AI总结：
本文利用广义函数定义非Lipschitz切子丛的对合性，并证明对数-Lipschitz情形下带尖锐正则性估计的Frobenius定理，给出局部同胚及其向量场张成结构。
摘要：
我们利用广义函数将对合性的定义推广到非Lipschitz切子丛。我们证明了当子丛为对数-Lipschitz时具有尖锐正则性估计的Frobenius定理：若$\mathcal V$是秩为$r$的对数-Lipschitz对合子丛，则对任意$\varepsilon>0$，局部存在同胚$Φ(u,v)$，使得$Φ,\frac{\partialΦ}{\partial u^1},\dots,\frac{\partialΦ}{\partial u^r}\in C^{0,1-\varepsilon}$，并且$\mathcal V$由连续向量场$Φ_*\frac\partial{\partial u^1},\dots,Φ_*\frac\partial{\partial u^r}$张成。
英文摘要：
We extend the definition of involutivity to non-Lipschitz tangent subbundles using generalized functions. We prove the Frobenius Theorem with sharp regularity estimate when the subbundle is log-Lipschitz: if $\mathcal V$ is a log-Lipschitz involutive subbundle of rank $r$, then for any $\varepsilon>0$, locally there is a homeomorphism $Φ(u,v)$ such that $Φ,\frac{\partialΦ}{\partial u^1},\dots,\frac{\partialΦ}{\partial u^r}\in C^{0,1-\varepsilon}$, and $\mathcal V$ is spanned by the continuous vector fields $Φ_*\frac\partial{\partial u^1},\dots,Φ_*\frac\partial{\partial u^r}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
