论文标题
定量稳定性以最大程度地减少Yamabe指标
Quantitative Stability for Minimizing Yamabe Metrics
论文作者
论文摘要
在任何封闭的riemannian dimensian $ n \ geq 3 $的封闭式歧管上，我们证明，如果功能几乎最小化yamabe能量，则相应的同源度度量在定量意义上是接近的，以最大程度地减少同条类中的Yamabe Metric。通常，该距离由Yamabe能量不足四次控制。最后，我们产生了一个二次估计值的示例。
On any closed Riemannian manifold of dimension $n\geq 3$, we prove that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close, in a quantitative sense, to a minimizing Yamabe metric in the conformal class. Generically, this distance is controlled quadratically by the Yamabe energy deficit. Finally, we produce an example for which this quadratic estimate is false.
