论文标题
公制规律性，伪 - 雅各布人和全球倒置定理关于Finsler歧管
Metric regularity, pseudo-Jacobians and global inversion theorems on Finsler manifolds
论文作者
论文摘要
本文我们的目的是研究本地Lipschitz地图$ f：x \至y $（可能是无限维度）鳍片歧管之间的全球不可逆性，这强调了与覆盖属性和$ f $的度量规则性的连接。为此，我们在这种情况下介绍了一个自然的假雅各布$ jf $，这是一种与$ f $相关的设置值差分对象。通过合适的索引，我们研究了伪jacobian $ jf $的属性与地图$ f $的本地度量属性之间的关系，这导致$ f $的条件成为覆盖地图，而对于$ f $来说是可逆的。特别是，在这种情况下，我们获得了Hadamard积分条件的版本。
Our aim in this paper is to study the global invertibility of a locally Lipschitz map $f:X \to Y$ between (possibly infinite-dimensional) Finsler manifolds, stressing the connections with covering properties and metric regularity of $f$. To this end, we introduce a natural notion of pseudo-Jacobian $Jf$ in this setting, as is a kind of set-valued differential object associated to $f$. By means of a suitable index, we study the relations between properties of pseudo-Jacobian $Jf$ and local metric properties of the map $f$, which lead to conditions for $f$ to be a covering map, and for $f$ to be globally invertible. In particular, we obtain a version of Hadamard integral condition in this context.
