We define a condition called almost strict domination for pairs of representations , , where is the isometry group of a Hadamard manifold, and prove that it holds if and only if one can find a -equivariant spacelike maximal surface in a certain pseudo-Riemannian manifold, unique up to fixing some parameters. The proof amounts to setting up and solving an interesting variational problem that involves infinite energy harmonic maps. Adapting a construction of Tholozan, we construct all such representations and parametrise the deformation space. When , an almost strictly dominating pair is equivalent to the data of an anti-de Sitter 3-manifold with specific properties. The results on maximal surfaces provide a parametrisation of the deformation space of such 3-manifolds as a union of components in a relative representation variety.

中文翻译：

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几乎严格的统治和反德西特3流形

我们为表示对定义一个称为几乎严格支配的条件,， 在哪里是阿达玛流形的等距群，并证明当且仅当我们能找到一个-某个伪黎曼流形中的等变空间最大曲面，在固定某些参数时是唯一的。该证明相当于建立并解决一个有趣的变分问题，其中涉及无限能量调和图。我们采用 Tholozan 的结构，构建所有此类表示并对变形空间进行参数化。什么时候，几乎严格支配对相当于具有特定属性的反德西特 3 流形的数据。最大表面上的结果提供了这种 3 流形的变形空间的参数化，作为一个组件的联合。相对代表性的多样性。