论文标题
Moser的方法和差异性的保守扩展
Moser's Method and Conservative Extensions of Diffeomorphisms
论文作者
论文摘要
本文应关注三个主要结果。经过简短的回忆，对基本的互合式几何形状进行了回忆，我们证明了使用Moser的同拷贝方法，例如在[HOR]的定理21.1.6中发现了强大的Darboux定理的特殊情况。接下来，我们将证明两个保守的扩展结果，用于圆圈上的差异性。一个人使用Moser的同型方法，但失去了一定程度的规律性。另一个使用[BCW]和[BGV]中发现的生成函数的方法。最后，我们将证明在$（0，1）^2 $边界上定义的“差异性”的保守扩展结果，并使用在此处开发的技术并通过[m]证明了环境dacarogna-moser定理。
This paper shall be concerned with three main results. After a brief recollection of basic symplectic geometry, we prove using Moser's homotopy method a special case of the Strong Darboux Theorem found, for instance, in Theorem 21.1.6 of [Hor]. Next, we'll prove two conservative extension results for a diffeomorphism on a circle. One uses Moser's homotopy method but loses a degree of regularity. The other uses the method of generating functions as found in [BCW] and [BGV]. Finally, we'll prove a conservative extension result for a "diffeomorphism" defined on the boundary of $(0, 1)^2$ and use the techniques developed there and by [M] to prove an ambient Dacarogna-Moser Theorem.
