Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes, Application to the Minkowski problem in the Minkowski space

Entire surfaces of constant curvature in Minkowski 3-space

This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by properly embedded convex surfaces of constant Gaussian curvature. This is a consequence of our classification of surfaces with bounded prescribed Gaussian curvature, sometimes called the Minkowski problem, for which partial results were obtained by Li, Guan-Jian-Schoen, and Bonsante-Seppi. Some applications to minimal Lagrangian self-maps of the hyperbolic plane…

利用高斯-博内定理研究具有渐近闵可夫斯基核心的旋转正则黑洞的光线弱弯曲

Weak Bending of Light by Rotating Regular Black Holes with Asymptotically Minkowski Core using the Gauss-Bonnet Theorem

本文利用高斯-博内定理研究具有渐近闵可夫斯基核心的旋转正则黑洞的弱引力透镜，计算了有限距离下的光线偏折角，分析了其与运动方向、 impact参数$b$的关系及与其他正则黑洞的相似性。

Strictly static spacetimes and positive mass in the Einstein-Gauss-Bonnet theory

In the Einstein gravity, it is well-known that strictly stationary and vacuum regular spacetime should be the Minkowski spacetime. In the Einstein-Gauss-Bonnet theory, we shall show the similar statement, that is, strictly static(no event horizon), vacuum and asymptotically flat spacetimes with conformally static slices are the Minkowski spacetime when the curvature corrections are small.

Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski Functionals

Despite the wealth of $Planck$ results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependencies. Aiming at detecting the NGs of the CMB temperature anisotropy $δT$, while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function $P(δT)$, related to ${\ma…

Minkowski (n+1) 空间中的完备 CMC 超曲面

Complete CMC hypersurfaces in Minkowski (n+1)-space

本文证明 Minkowski 空间任意正则区域存在唯一的类空 CMC 超曲面叶层结构，完成整类空 CMC 超曲面分类，并据此得到 2+1 维常 Gauss 曲率整曲面与双曲平面直凸区域等距。

Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector field vanishes. In particular, a local description of marginally trapped surfaces invariant under spacelike rotations is exhibited.