论文标题
在具有边界和应用的歧管上的BACH-FLAT指标的刚度
Rigidity for Bach-flat metrics on manifolds with boundary and applications
论文作者
论文摘要
在文章中，我们考虑了具有边界的四个manifolds上的BACH-FLAT指标，具有不变的边界条件。我们表明，这种指标自然是在约束下作为Weyl能量的临界点。然后，我们证明了一个刚性结果：如果限制到边界时与临界度量相关的Yamabe度量是等于三轮圆形的等级，则临界度量必须与标准的上半球等轴测。
In the article we consider Bach-flat metrics on four-manifolds with boundary, with conformally invariant boundary conditions. We show that such metrics arise naturally as critical points of the Weyl energy under a constraint. We then prove a rigidity result: if a Yamabe metric associated to a critical metric when restricted to the boundary is isometric to the round three-sphere, then the critical metric must be isometric to the standard upper hemisphere.
