Plateau问题一直以来都是几何测度论的一个核心问题，它推动着几何测度论的发展。但是由于缺乏新的工具出现，近些年来少有进展。然而，自从2013年Guy David提出sliding boundary Plateau问题之后，又涌现了新的途径，沿此途径，我门将探索sliding almost 极小集的正则性，通过这类集合的正则性来解决sliding boundary Plateau问题的存在性。

Plateau’s problem, which is very important in the development of geometric measure theory, is a core topic in the domain. We have made very little progress in Plateau’s problem in recent years due to no appearance of new techniques. However, Guy David proposed the sliding boundary Plateau Problem in 2013. In the point of view of sliding boundary, we have new perspectives. We will firstly study the regularity of sliding almost minimal sets, then by the regularity we may approach the existence of the sliding boundary Plateau Problem.