We prove an ‘h-principle without pre-conditions’ for the elimination of tangencies of a Lagrangian submanifold with respect to a Lagrangian distribution. The main result states that such tangencies can always be completely removed at the cost of allowing the Lagrangian to develop certain non-smooth points, called Lagrangian ridges, modeled on the corner $\{p=|q|\}\subset {\mathbb{R}}^2$$\{p=|q|\}\subset {\mathbb{R}}^2$ together with its products and stabilizations. This result plays an essential role in the arborealization program.

中文翻译：

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拉格朗日脊地貌

我们证明了一个“无先决条件的 h 原理”，用于消除拉格朗日子流形相对于拉格朗日分布的切线。主要结果表明，这种切线总是可以完全消除，但代价是允许拉格朗日函数发展某些非光滑点，称为拉格朗日脊，以拐角为模型$\{p=|q|\}\subset {\mathbb{R}}^2$$\{p=|q|\}\subset {\mathbb{R}}^2$连同其产品和稳定剂。这一结果在树栖计划中起着至关重要的作用。