Uniqueness of H-surfaces in H^2xR, |H| <= 1/2, with boundary one or two parallel horizontal circles

关于平移曲面上某些类型圆堆积的唯一性

On the Uniqueness of Certain Types of Circle Packings on Translation Surfaces

本文证明在 $H(1,1)$ 平移曲面上，固定割缝两圆盘时，某些圆堆积在不改变接触图的前提下仅有有限种变化，并利用分裂双角刻画这些变化，进而推广到任意亏格 $g \geq 2$ 的特定曲面。

A characterization of gauge balls in $\mathbb{H}^n$ by horizontal curvature

In this paper we aim at identifying the level sets of the gauge norm in the Heisenberg group $\mathbb{H}^n$ via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in $\mathbb{H}^1$ under an assumption on the location of the singular set, and in $\mathbb{H}^n$ for $n\geq 2$ in the proper class of horizontally umbilical hypersurfaces

Geometric finiteness and uniqueness for Kleinian groups with circle packing limit sets

In this paper, we assume that $G$ is a finitely generated torsion free non-elementary Kleinian group with $Ω(G)$ nonempty. We show that the maximal number of elements of $G$ that can be pinched is precisely the maximal number of rank 1 parabolic subgroups that any group isomorphic to $G$ may contain. A group with this largest number of rank 1 maximal parabolic subgroups is called {\it maximally parabolic}. We show such groups exist. We state our main theorems concisely here. Theorem I. The limit set of a maximally parabolic group is a circle packing; that is, every component of its regular set…

Uniqueness of generalized p-area minimizers and integrability of a horizontal normal in the Heisenberg group

We study the uniqueness of generalized $p$-minimal surfaces in the Heisenberg group. The generalized $p$-area of a graph defined by $u$ reads $\int |\nabla u+\vec{F}| + Hu$. If $u$ and $v$ are two minimizers for the generalized $p$-area satisfying the same Dirichlet boundary condition, then we can only get $N_{\vec{F}}(u)$ $=$ $N_{\vec{F}}(v)$ (on the nonsingular set) where $N_{\vec{F}}(w)$ $:=$ $\frac{\nabla w+\vec{F}}{|\nabla w+\vec{F}|}.$ To conclude $u$ $=$ $v$ (or $\nabla u$ $=$ $\nabla v)$, it is not straightforward as in the Riemannian case, but requires some special argument in general…

$\mathbb{CP}^2$ 中嵌入极小拉格朗日环面的唯一性

Uniqueness of embedded minimal Lagrangian tori in $\mathbb{CP}^2$

本文证明复射影平面中任意嵌入极小拉格朗日环面必全等于克利福德环面，方法为利用五维球面归一化水平提升构造两点函数。

Dirichlet能量的常各向异性均曲率 stationary 面的圆柱面

Circles-foliated stationary surfaces of the Dirichlet energy

研究了欧几里得空间中具有常各向异性均曲率Λ的Dirichlet能量∫_Ω(|Du|²+Λu)的曲面，证明了Λ=0时存在非旋转曲面，由包含水平平面的圆柱面构成，扩展了极小面理论到各向异性Dirichlet能量的框架。