论文标题
$ p $ harmonic功能的单调量及其应用
Monotone quantities of $p$-harmonic functions and their applications
论文作者
论文摘要
我们在具有非负标态曲率的流形上得出了与$ p $ harmonic功能相关的本地和全局单调量。作为应用程序，我们获得了有关渐近平面$ 3 $ manifolds，$ p $ copacity和Willmore功能的不平等现象。作为$ p \至1 $，其中一个结果检索了经典的关系，如果表面是外部最小化的面积，则ADM质量会占主导地位。
We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the $p$-capacity and the Willmore functional of the boundary. As $ p \to 1$, one of the results retrieves a classic relation that the ADM mass dominates the Hawking mass if the surface is area outer-minimizing.
