标题： 欧几里得空间中正常图的几何及其在闵可夫斯基空间中的Penrose不等式应用 显示英文标题

标题： Geometry of normal graphs in Euclidean space and applications to the Penrose inequality in Minkowski

摘要： 在闵可夫斯基时空中的Penrose不等式是一个几何不等式，它将闭合、连通和类空的余维二曲面S在闵可夫斯基时空中与总外零扩张和面积相关联，并且需要满足一个额外的凸性假设。 在最近的一篇论文中，Brendle和Wang找到了这个Penrose不等式有效性的充分条件，该条件基于S在常时间超平面上的正交投影的几何性质。 在这项工作中，我们研究了n维欧几里得空间中作为其他曲面的法图的超曲面的几何性质，并将图的内在和外在几何与基底超曲面的几何联系起来。 这些结果被用来以S在超平面上的时间高度函数以及沿其过去零锥投影到该超平面的投影几何来明确地重写Brendle和Wang的条件。 我们还在附录中包含了一个关于严格静态时空中余维二类空曲面沿Killing方向投影的几何性质的已知和新结果的自包含总结。 显示英文摘要

摘要： The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang find a sufficient condition for the validity of this Penrose inequality in terms of the geometry of the orthogonal projection of S onto a constant time hyperplane. In this work, we study the geometry of hypersurfaces in n-dimensional euclidean space which are normal graphs over other surfaces and relate the intrinsic and extrinsic geometry of the graph with that of the base hypersurface. These results are used to rewrite Brendle and Wang's condition explicitly in terms of the time height function of S over a hyperplane and the geometry of the projection of S along its past null cone onto this hyperplane. We also include, in an Appendix, a self-contained summary of known and new results on the geometry of projections along the Killing direction of codimension two-spacelike surfaces in a strictly static spacetime.