Finsler流形上非光滑映射的整体反演
Global inversion of nonsmooth mappings on Finsler manifolds
摘要：
本文研究了Finsler流形之间的局部Lipschitz映射是整体同胚的充分条件的问题。为了这个目的，我们开发的概念，克拉克广义微分在这种情况下，使用这个，我们得到一个版本的阿达玛积分条件可逆性。作为推论，我们利用Lipschitz映射的Clarke广义微分的谱条件，得到了$\mathbb{R}^n$上Lipschitz映射的整体反演和整体内射性结果.
英文摘要：
We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, using this, we obtain a version of the Hadamard integral condition for invertibility. As consequences, we deduce some global inversion and global injectivity results for Lipschitz mappings on $\mathbb{R}^n$ in terms of spectral conditions of its Clarke generalized differential.
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