论文标题
log-lipschitz子捆绑的Frobenius定理
The Frobenius Theorem for Log-Lipschitz Subbundles
论文作者
论文摘要
我们使用广义函数扩展了对非lipschitz切线子捆绑的定义。当Subbundle为log-lipschitz时，我们证明了Frobenius定理的规律性估计：如果$ \ \ \ \ m rathcal v $是log-lipschitz的log-lipschitz complate cang $ r $ r $ r $的参与分支，那么对于任何$ \ varepsilon> 0 $，在本地，有一个同源性$ m（u，v）$（u，v）$（u，v） $φ，\ frac {\partialφ} {\ partial u^1}，\ dots，\ frac {\partialφ} {\ partial u^r} \ in c^{0,1- \ \ varepsilon} $ in C^{0,1- \ varepsilon} $，以及$ \ \ \ Mathcal v $ spand v $ spand v $ spand v $ $φ_*\ frac \ partial {\ partial u^1}，\ dots，φ_*\ frac \ partial {\ partial u^r} $。
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 $Φ_*\frac\partial{\partial u^1},\dots,Φ_*\frac\partial{\partial u^r}$.
