Einstein-de Sitter时空中的完备常平均曲率类空超曲面

Free data at spacelike $\mathscr{I}$ and characterization of Kerr-de Sitter in all dimensions

We study the free data in the Fefferman-Graham expansion of asymptotically Einstein metrics with non-zero cosmological constant. We prove that if $\mathscr{I}$ is conformally flat, the rescaled Weyl tensor at $\mathscr{I}$ agrees up to a constant with the free data at $\mathscr{I}$ , namely the traceless part of the $n$-th order coefficient of the expansion. In the non-conformally flat case, the rescaled Weyl tensor is generically divergent at $\mathscr{I}$ but one can still extract the free data in terms of the difference of the Weyl tensors of suitably constructed metrics, in full generality…

扩展Schwarzschild时空中的类空球对称CMC叶理

Spacelike spherically symmetric CMC foliation in the extended Schwarzschild spacetime

首先总结了Schwarzschild时空和Kruskal扩张中光滑类空球对称常数中曲率（SS-CMC）超曲面的特征。然后利用这一刻画证明了SS-CMC的特殊叶理性质，并验证了Malec和Murchadha在2003年论文中的部分猜想。

内在的海森堡型下界在广义相对论中的类空超曲面

Intrinsic Heisenberg-type lower bounds on spacelike hypersurfaces in general relativity

研究通过投影定位和几何方法，在广义相对论中推导出类空超曲面上的海森堡型动量-位置下界。

渐近Anti-de Sitter空间中线性波动方程的零-类时边值问题

The Null-Timelike Boundary Problems of Linear Wave Equations in Asymptotically Anti-de Sitter Space

本文研究了渐近反de Sitter时空中的线性波动方程。我们将考虑混合边值问题，其中初始数据在一个输出零超曲面和一个类时超曲面上给出，渐近信息在共形无穷大上给出。

时空中具有因果中曲率向量场的类空子流形的刚性和不存在性及广义相对论中的Cauchy问题

Rigidity and non-existence of spacelike submanifolds with causal mean curvature vector field in spacetimes and the Cauchy problem in General Relativity

给出了时空中类空子流形的不存在性和刚性的新的一般结果，其中时空的中曲率是面向时间的因果向量场。这些结果适用于广泛的一类时空，其中包括全球双曲时空，静止时空，共形静止时空和PP波时空等。此外，应用广义相对论中的柯西问题。最后，在超曲面的情况下，我们也得到了重要的后果，在几何分析，解决新的Calabi-Bernstein和狄利克雷问题的黎曼流形。

From holography to the geometry of the spacetime

We show the geometric consequences that the holographic principle has on the spacetime. Namely, we prove that complete spacelike hypersurfaces in a spacetime that satisfies the holographic principle are non-parabolic. This has important consequences on the behaviour of the Brownian motion in these spacelike hypersurfaces, as well as provides a method for finding examples of universes that lead to a violation of this principle.

无类空奇点的黑洞

Black holes without spacelike singularities

结果表明，对于Einstein-Maxwell-real标量场系统渐近平坦的两端Reissner-Nordström数据的小的球对称扰动，演化的动态时空的边界全局地表示为一个分叉的零超曲面，度规在该超曲面上连续延伸.在附加的假设下，证明了Hawking质量沿这个分叉零超曲面同向爆破，从而度规不能作二次可微扩张，事实上，不能在Christoffel符号的水平上作较弱的扩张.证明结合了在以前的工作中获得的估计与一个基本的柯西稳定性参数。对标量场的支撑的大小没有限制，并且结果适用于时空的未来和过去边界。特别地，它得出结论，对于Reissner-Nordström周围解的模空间中的开集，未来或过去奇点都不存在类空分量。

黎曼流形和半黎曼流形上的CMC超曲面

CMC hypersurfaces on riemannian and semi-riemannian manifolds

本文给出了常截面曲率的半黎曼流形中几类常平均曲率和非常主曲率浸入的显式例子。特别地，我们证明了[-1，-2 sqrt{n-1}/n）中的每个h都可以实现为（n+1）维de Sitter空间S_1^{n+1}中S_1 ^{n-1} x R的完全浸入的常曲率.我们给出了Minkowski空间中的3类cmc浸入、de Sitter空间中的5类cmc浸入和反de Sitter空间中的5类cmc浸入.在文章的最后，我们分析了家庭的例子，可以扩展到封闭的超曲面。

Hyperbolic Metamaterials and Massive Klein-Gordon Equation in 2+1 Dimensional de Sitter Spacetime

The wave equation obeyed by the extraordinary component of the electric field in a hyperbolic metamaterial was shown to be a massless Klein-Gordon field living in a flat spacetime with two timelike and two spacelike dimensions. Such a wave equation, unexpectedly, allows dispersionless propagation albeit having two spatial dimensions. Here we show that the same equation can be naturally interpreted as a particular massive Klein-Gordon equation with the usual one timelike and two spacelike dimensions in a de Sitter (dS) background spacetime. The mass parameter of the scalar field is given in ter…

Mean curvature flow in null hypersurfaces and the detection of MOTS

We study the mean curvature flow in 3-dimensional null hypersurfaces. In a spacetime a hypersurface is called null, if its induced metric is degenerate. The speed of the mean curvature flow of spacelike surfaces in a null hypersurface is the projection of the codimension-two mean curvature vector onto the null hypersurface. We impose fairly mild conditions on the null hypersurface. Then for an outer un-trapped initial surface, a condition which resembles the mean-convexity of a surface in Euclidean space, we prove that the mean curvature flow exists for all times and converges smoothly to a ma…

扩展Schwarzschild时空中常中曲率叶理的存在性

Existence of constant mean curvature foliation in the extended Schwarzschild spacetime

我们构造了一个$T$ -轴对称的，类空的，球对称的，常数中曲率的超曲面叶状的Kruskal扩展的性质，中曲率变化在每个切片和范围从负无穷大到正无穷大。这个超曲面家族扩展了Malec和Mr. Murchadha在2009年发表的CMC叶理讨论。

渐近de Sitter时空的正质量定理

Positive mass theorems for asymptotically de Sitter spacetimes

我们使用平面坐标和双曲坐标将德西特时空分成两部分。这两种切割德西特的方法产生了两种不同的空间无限性。对于渐近于德西特时空的任意一半的时空，我们能够分别给出总能量、总线动量和总角动量的定义。对于中曲率由上述常数限定的类空超曲面，我们证明了与这两类空间无穷大相对应的两个正质量定理。