数学物理、整体分析和光谱几何中的细管
Thin tubes in mathematical physics, global analysis and spectral geometry
摘要：
细管是一个$n$维空间，它在$n-1$方向上比其余方向非常薄，例如，对于小的$ε$，曲线的$ε$邻域或$\R^n$中的嵌入图。在不同的背景下研究了细管上的拉普拉斯算子和相关算子，有不同的目标，但重叠的技术。在这次调查中，我们解释了其中的一些背景，方法和结果，希望鼓励标题中提到的学科之间更多的互动。
英文摘要：
A thin tube is an $n$-dimensional space which is very thin in $n-1$ directions, compared to the remaining direction, for example the $ε$-neighborhood of a curve or an embedded graph in $\R^n$ for small $ε$. The Laplacian on thin tubes and related operators have been studied in various contexts, with different goals but overlapping techniques. In this survey we explain some of these contexts, methods and results, hoping to encourage more interaction between the disciplines mentioned in the title.
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。
