论文标题
最小表面和CPE度量
Minimal surfaces and CPE metric
论文作者
论文摘要
总标度曲率功能的临界点，仅限于具有恒定标量曲率指标和单位体积的封闭$ n $二维流形，称为CPE指标。 1987年，亚瑟·贝塞（Arthur L. Besse）猜想CPE指标始终是爱因斯坦（Einstein）。使用最小表面的理论，我们证明了具有$ c^\ infty $ generic riemannian公制的三维流形的猜想。
The critical points of the total scalar curvature functional, restricted to closed $n$-dimensional manifolds with constant scalar curvature metrics and unit volume, are termed CPE metrics. In 1987, Arthur L. Besse conjectured that CPE metrics are always Einstein. Using the theory of minimal surfaces, we prove the conjecture for three-dimensional manifolds with $C^\infty$-generic Riemannian metric.
