光滑流形上分布芽的重构定理
Reconstruction Theorem for Germs of Distributions on Smooth Manifolds
摘要：
重构定理是正则结构理论的基石[Hai14]。在[CZ 20]中，作者在欧氏空间$\mathbb{R}^d$上用分布理论的语言表述并证明了这个结果，而没有参考原始的框架。在本文中，我们推广他们的建设的情况下，分布一般$d$维光滑流形$M$，证明重建定理在这种设置。这样做是考虑到扩展的理论的正则结构顺利流形。
英文摘要：
The reconstruction theorem is a cornerstone of the theory of regularity structures [Hai14]. In [CZ20] the authors formulate and prove this result in the language of distributions theory on the Euclidean space $\mathbb{R}^d$, without any reference to the original framework. In this paper we generalize their constructions to the case of distributions over a generic $d$-dimensional smooth manifold $M$, proving the reconstruction theorem in this setting. This is done having in mind the extension of the theory of regularity structures to smooth manifolds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
