Study of deformation of group actions from various viewpoints

我们从不同的角度研究了群体行为的变形，主要是从几何和动力学的角度。从几何角度，我们证明了球体上的自然共形作用只允许共形变形。我们还将此结果中使用的方法应用于环面上的另一个操作。我们证明了对保留几何结构的环面的作用只允许保留相同类型几何结构的变形。从动力学方面，我们从动作的扩展性的角度重新解释了群体动作的几个已知的刚性结果

We studied deformation of group actions from various viewpoints, mainly from geometric and dynamical view points. From geometric side, we proved that a natural conformal action on the sphere admits only conformal deformation. We also applied the method used in this result to another action on the torus. We proved an action on the torus which preserves a geometric structure admits only deformation which preserves the same type of geometric structure. From dynamical side, we reinterpreted several known rigidity results on group actions from the viewpoint of expansion property of the actions