论文标题
椭圆形温达尔滕表面：奇点，旋转示例和半空间定理
Elliptic Weingarten surfaces: singularities, rotational examples and the halfspace theorem
论文作者
论文摘要
我们通过阶段空间分析表明，在$ \ mathbb {r}^3 $中，旋转表面完全有17个可能的定性行为，使得满足任意椭圆形的weingarten方程$ W（κ_________2，κ_2）= 0 $，并研究了此类示例的奇异性。作为该分类的全球应用，我们证明了有限顺序的一般椭圆形温度方程的尖锐半空间定理，以及最多有两个奇异性的峰值椭圆形温达尔登球体的分类。如果$ w $不是椭圆机，那么我们对Yau的问题给出了负面答案，以了解旋转椭圆形的独特性。
We show by phase space analysis that there are exactly 17 possible qualitative behaviors for a rotational surface in $\mathbb{R}^3$ that satisfies an arbitrary elliptic Weingarten equation $W(κ_1,κ_2)=0$, and study the singularities of such examples. As global applications of this classification, we prove a sharp halfspace theorem for general elliptic Weingarten equations of finite order, and a classification of peaked elliptic Weingarten spheres with at most two singularities. In the case that $W$ is not elliptic, we give a negative answer to a question by Yau regarding the uniqueness of rotational ellipsoids.
