论文标题
关键电容器的渐近末端叶子
Foliation of an asymptotically flat end by critical capacitors
论文作者
论文摘要
我们构建了一个由高空曲面的渐近平坦端的叶面，这是潜在理论中自然功能的关键点。这些超曲面是大坐标球的扰动，它们接纳了涉及拉普拉斯 - 贝特拉米操作员的某些过度确定的边界价值问题的解决方案。在一个关键步骤中，我们必须倒转到dirichlet到Neumann运营商，突出我们问题的非本地性质
We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace-Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the non-local nature of our problem
