Delaunay surfaces of prescribed mean curvature in $\mathrm{Nil}_3$ and $\widetilde{SL_2}(\mathbb{R})$

Height estimates for constant mean curvature graphs in $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$

In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$. As a straightforward consequence, we announce a structure-type result for proper graphs defined on relatively compact domains.

$Nil^{4}$中Codazzi超曲面的分类及极小超曲面注记

Classification of Codazzi and note on minimal hypersurfaces in $Nil^{4}$

本文研究李群$(Nil^{4},\tilde{g})$中的超曲面问题，完成了Codazzi超曲面的分类，刻画了一类极小超曲面并给出实例，丰富了该空间的超曲面理论。

非负Ricci曲率、幂零性与Hausdorff维数

Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension

本文证明非负Ricci曲率且逃逸率非1/2的开放流形，其基本群的幂零步长可由万有覆盖渐近锥中某等距R轨道的Hausdorff维数下界刻画，解决了Wei与作者的问题。

Lorentzian left invariant metrics on three dimensional unimodular Lie groups and their curvatures

There are five unimodular simply connected three dimensional unimodular non abelian Lie groups: the nilpotent Lie group $\mathrm{Nil}$, the special unitary group $\mathrm{SU}(2)$, the universal covering group $\widetilde{\mathrm{PSL}}(2,\mathbb{R})$ of the special linear group, the solvable Lie group $\mathrm{Sol}$ and the universal covering group $\widetilde{\mathrm{E}_0}(2)$ of the connected component of the Euclidean group. For each $G$ among these Lie groups, we give explicitly the list of all Lorentzian left invariant metrics on $G$, up to un automorphism of $G$. Moreover, for any Lorentz…

在 $\mathbb{H}^2\times\mathbb{R}$ 中常平均曲率曲面的构造及 Krust 性质

A construction of constant mean curvature surfaces in $\mathbb{H}^2\times\mathbb{R}$ and the Krust property

本文构造了 $\mathbb{H}^2\times\mathbb{R}$ 中一族常平均曲率曲面，推广了鞍形塔和 $k$-noids，并证明 Krust 性质对任何 $H>0$ 不成立。

Constant mean curvature $k$-noids in homogeneous manifolds

For each $k\geq2$, we construct two families of surfaces with constant mean curvature $H$ for $H\in[0,1/2]$ in $Σ(κ)\times\R$ where $κ+4H^2\leq0$. The surfaces are invariant under $2π/k$-rotations about a vertical fiber of $Σ(κ)\times\R$, have genus zero, and a finite number of ends. The first family generalizes the notion of $k$-noids: It has $k$ ends, one horizontal and $k$ vertical symmetry planes. The second family is less symmetric and has two types of ends. Each surface arises as the conjugate (sister) surface of a minimal graph in a homogeneous 3-manifold. The domain of the graph is non…