Liouville domains have become central objects in symplectic and contact geometry. However, the auxiliary data they involve --- namely, Liouville forms --- and the non-compactness of their completions generate some inconvenience. The notion of ideal Liouville domains is designed to suppress these awkward aspects and to let symplectic structures play the leading role. Ideal Liouville domains are compact manifolds with boundary whose interior carries a symplectic form satisfying some tameness condition along the boundary. Their definition and their basic properties are presented in the first part of these notes, while the second part discusses their relevance in contact geometry.

中文翻译：

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理想的 Liouville Domains，一个很酷的小工具

Liouville 域已成为辛几何和接触几何的中心对象。然而，它们所涉及的辅助数据——即Liouville形式——以及它们完成的非紧凑性产生了一些不便。理想刘维尔域的概念旨在抑制这些尴尬的方面并让辛结构发挥主导作用。理想的 Liouville 域是具有边界的紧凑流形，其内部带有满足沿边界的某种驯服条件的辛形式。这些注释的第一部分介绍了它们的定义和基本属性，而第二部分讨论了它们在接触几何中的相关性。