In this paper we investigate the boundary behavior of finitely bi-Lipschitz homeomorphisms between Finsler manifolds. Our study involves the module technique and classes of mappings whose moduli of the curve/surface families are integrally controlled from above and below. The Lusin (N)-property with respect to the k-dimensional Hausdorff measure for the finitely bi-Lipschitz mappings is also established.

中文翻译：

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Finsler流形之间的有限双Lipschitz同胚

在本文中，我们研究了Finsler流形之间有限双Lipschitz同胚的边界行为。我们的研究涉及模块技术和映射类别，这些类别的曲线/曲面族的模量是从上方和下方进行整体控制的。还建立了关于有限双Lipschitz映射的k维Hausdorff测度的Lusin（N）属性。