Stationary rotating surfaces in Euclidean space

Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in complex Euclidean plane

We classify all Hamiltonian stationary Lagrangian surfaces in complex Euclidean plane which are self-similar solutions of the mean curvature flow.

A criterion on instability of rotating cylindrical surfaces

We consider a column of a rotating stationary surface in Euclidean space. We obtain a value $l_0>0$ in such way that if the length $l$ of column satisfies $l>l_0$, then the surface is instable. This extends, in some sense, previous results due to Plateau and Rayleigh for columns of surfaces with constant mean curvature.

指标为2的伪欧氏4空间中旋转曲面的研究

The Research on Rotational Surfaces in pseudo Euclidean 4-space with index 2

该研究在4维半欧氏空间中，通过曲线与矩阵定义双曲、椭圆型旋转曲面，构造对应子群的两类参数旋转矩阵并生成旋转曲面，丰富了伪欧氏空间旋转曲面的研究内容。

Bernstein type theorems for spacelike stationary graphs in Minkowski spaces

For entire spacelike stationary 2-dimensional graphs in Minkowski spaces, we establish Bernstein type theorems under specific boundedness assumptions either on the W-function or on the total (Gaussian) curvature. These conclusions imply the classical Bernstein theorem for minimal surfaces in 3-dimensional Euclidean space and Calabi's theorem for spacelike maximal surfaces in 3-dimensional Minkowski space.

Asymptotically Locally Euclidean/Kaluza-Klein Stationary Vacuum Black Holes in 5 Dimensions

We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in 5 dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean in which spatial cross-sections at infinity have lens space $L(p,q)$ topology, or asymptotically Kaluza-Klein so that spatial cross-sections at infinity are topologically $S^1\times S^2$. These are nondegenerate black holes of cohomogeneity 2, with any number of horizon components, where the horizon cross-section topology is any one of the three admissible types: $S^3$, $S^1\times S^2$, or $…

The classification of complete stable area-stationary surfaces in the Heisenberg group $\mathbb{H}^1$

We prove that any $C^2$ complete, orientable, connected, stable area-stationary surface in the sub-Riemannian Heisenberg group $\mathbb{H}^1$ is either a Euclidean plane or congruent to the hyperbolic paraboloid $t=xy$.