论文标题
具有谐波电势的亚静态歧管的几何电容性不等式
A geometric capacitary inequality for sub-static manifolds with harmonic potentials
论文作者
论文摘要
在本文中，我们证明了与谐波潜力的近静态渐变平坦的歧管相关联，有一个单参数家族$ \ {f_β\} $的函数，它们沿电势级流动是单调的。这样的单调性能达到最佳阈值$β= \ frac {n-2} {n-1} $，并允许我们证明几何学电容性不平等，其中地平线的能力在著名的Riemannian Penrose不平等中起着与ADM质量相同的作用。
In this paper, we prove that associated with a sub-static asymptotically flat manifold endowed with a harmonic potential there is a one-parameter family $\{F_β\}$ of functions which are monotone along the level-set flow of the potential. Such monotonicity holds up to the optimal threshold $β=\frac{n-2}{n-1}$ and allows us to prove a geometric capacitary inequality where the capacity of the horizon plays the same role as the ADM mass in the celebrated Riemannian Penrose Inequality.
