Some properties of surfaces of finite III-type

模空间III上具有对合、等变解析挠率和自守形式的K3曲面：r（M）\geq 18情形

K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space III: the case r(M)\geq18

在模空间的维数小于或等于2的情况下，证明了利用等变解析挠得到的对合K3曲面的不变量的自守性质。

Willmore surfaces in spheres via loop groups III: on minimal surfaces in space forms

The family of Willmore immersions from a Riemann surface into $S^{n+2}$ can be divided naturally into the subfamily of Willmore surfaces conformally equivalent to a minimal surface in $\R^{n+2}$ and those which are not conformally equivalent to a minimal surface in $\R^{n+2}$. On the level of their conformal Gauss maps into $Gr_{1,3}(\R^{1,n+3})=SO^+(1,n+3)/SO^+(1,3)\times SO(n)$ these two classes of Willmore immersions into $S^{n+2}$ correspond to conformally harmonic maps for which every image point, considered as a 4-dimensional Lorentzian subspace of $\R^{1,n+3}$, contains a fixed lightlik…

若干极大对称$(2,3,5)$-分布的局部等价性 III：在平面上滚动的An-Nurowski曲面

Local equivalence of some maximally symmetric $(2,3,5)$-distributions III: An-Nurowski surface rolling on a plane

本研究分析An-Nurowski曲面与平面乘积上的圆扭量丛对应的极大对称$(2,3,5)$-分布，计算定义分裂$\frak{g}_2$李代数的相关向量场，推导得到$SL(3,\bR)$在子流形$\bR^2\times \bS^1$上的作用。

Ruled and quadric surfaces of finite Chen-type

In this paper, we study ruled surfaces and quadrics in the 3-dimensional Euclidean space which are of finite $III$-type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids and spheres are the only ruled and quadric surfaces of finite $III$-type, respectively.

中曲率流下完全嵌入自相似曲面的构造。部件III

Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part III

我们提出了新的例子完全嵌入自相似曲面下的中曲率通过胶合球和平面。这些表面具有有限的亏格，并且是$\mathbb R^3$中非旋转对称的自收缩体的第一个例子。其构造策略是通过对球面与平面的交线进行去奇异化，得到初始曲面族，然后通过求解扰动问题得到单参数自相似曲面族.虽然我们从在无穷远处渐近于无穷远平面的曲面开始，但构造的自相似曲面在无穷远处渐近于圆锥。

On the Lie and Cartan Theory of Invariant Differential Systems, III

It is presently our aim to undertake the discussion, of the Parts I and II, on the infinitesimal level and outline as well the transition from infinitesimal to finite, the main reason for this being, of course, the well known fact that arguments and calculation on the infinitesimal level are far simpler that those on the finite level.

多面体曲面的刚性，III

Rigidity of Polyhedral Surfaces, III

本文研究了包括反距离圆填充在内的多面体曲面的几个整体刚性问题。倒距离圆填充是由P. Bowers和K. Stephenson是Andreev-Thurston圆填充的推广。他们证明了反距离圆填料是刚性的。利用R. Guo在变分原理的基础上，结合倒距离圆填充，证明了Bowers-Stephenson的刚性猜想。我们还表明，每个多面体度量的三角化表面上的各种离散曲率所确定的在我们以前的工作，验证了猜想\cite{Lu1}。因此，我们表明，离散拉普拉斯算子确定了欧氏多面体度量缩放。

N维孤子方程是Self-dual Yang-Mills方程III的精确约化. 2+1和3+1维空间中的孤子几何

Soliton equations in N-dimensions as exact reductions of Self-dual Yang-Mills equation III. Soliton geometry in 2+1 and 3+1 dimensions

讨论了曲线曲面微分几何与多维孤子方程之间的某些关系。研究了多维孤子方程与自对偶杨-米尔斯方程之间的联系。

三维流形III中的嵌入极小曲面空间;平面域

The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains

本文是第三次在一个系列中，我们描述了空间的所有嵌入的极小曲面的固定属在一个固定的（但任意的）封闭的3-流形。在[CM 3]-[CM 5]中，我们描述了曲面在任何固定的小尺度上都是拓扑圆盘的情况。为了描述一般的平面区域（在[CM 6]中），除了[CM 3]-[CM 5]的结果之外，我们还需要嵌入稳定环的关键估计，这是本文的主要结果。这个估计断言，这样的环是一个图形远离其边界，如果它只有一个内部边界组件，如果这个组件位于一个小（外在）球。

Projective superflows. III. Finite subgroups of $U(2)$

Let $X\in\mathbb{R}^{n}$ or $\mathbb{C}^{n}$. For $ϕ:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$ (respectively, $ϕ:\mathbb{C}^{n}\mapsto\mathbb{C}^{n}$) and $t\in\mathbb{R}$ (respectively, $\mathbb{C}$), we put $ϕ^{t}=t^{-1}ϕ(Xt)$. A projective flow is a solution to the projective translation equation $ϕ^{t+s}=ϕ^{t}\circϕ^{s}$, $t,s\in\mathbb{R}$ or $\mathbb{C}$. The projective superflow is a projective flow with a rational vector field which, among projective flows with a given symmetry, is, up to a homothety, unique and optimal. In the first and the second part of this work we classified real $2$ a…