因果变分原理的$\boldsymbol{\tilde{\textit{L}}}$演算：非光滑空间上的外微分演算
The $\mathcal{L}$-Calculus for Causal Variational Principles: An Exterior Differential Calculus on Non-Smooth Spaces
AI总结：
本文针对非光滑空间，开发了适用于因果变分原理的$\boldsymbol{\tilde{\textit{L}}}$演算，将外微分演算及相关拓扑结构推广至非光滑空间，证明了斯托克斯定理等相关定理并辅以示例说明。
AI中文摘要：
本文开发了适用于因果变分原理的微分演算，该演算将微分形式的外演算及相关部分微分拓扑结构推广至非光滑空间。该演算包含外导数、de Rham上同调、粘合构造（微分形式的限制与扩张、Mayer-Vietoris序列）、Künneth公式及庞加莱引理，还证明了斯托克斯定理与高斯散度定理的对应版本，相关构造与结果通过多个示例进行了阐释。
英文摘要：
A differential calculus for causal variational principles is developed, which generalizes the exterior calculus of differential forms and some of the associated differential topological structures to non-smooth spaces. Our calculus includes the exterior derivative, de Rham cohomology, glueing constructions (restrictions and extensions of differential forms, Mayer-Vietoris sequence), a Künneth formula and Poincar{é}'s lemma. Moreover, we prove versions of Stokes' theorem and the Gauß divergence theorem. The constructions and results are illustrated by several examples.
