论文标题
$ \ mathbb {r}^3 $中规定的线性weingarten曲率的表面
Surfaces of prescribed linear Weingarten curvature in $\mathbb{R}^3$
论文作者
论文摘要
给定$ a，b \ in \ mathbb {r} $和$φ\ in c^1（\ mathbb {s}^2）$，我们研究了浮力3级$ \ \ m iuclidean 3-space $ \ mathbb {r}^3 $ curvature corvus $ h $ h $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ k y $ k $ k $ k y $ k $ k y $ k $ k = $ n：σ\ rightarrow \ mathbb {s}^2 $是高斯地图。该理论广泛概括了一些最重要的重要性，例如恒定均值和高斯曲率表面，线性魏因丁表面和平均曲率流的自变压孤子。在对规定函数$φ$的轻度假设下，我们对旋转表面的分类结果显示，在控制这些表面的基础完全非线性PDE是椭圆形的或双曲的。
Given $a,b\in\mathbb{R}$ and $Φ\in C^1(\mathbb{S}^2)$, we study immersed oriented surfaces $Σ$ in the Euclidean 3-space $\mathbb{R}^3$ whose mean curvature $H$ and Gauss curvature $K$ satisfy $2aH+bK=Φ(N)$, where $N:Σ\rightarrow\mathbb{S}^2$ is the Gauss map. This theory widely generalize some of paramount importance such as the ones constant mean and Gauss curvature surfaces, linear Weingarten surfaces and self-translating solitons of the mean curvature flow. Under mild assumptions on the prescribed function $Φ$, we exhibit a classification result for rotational surfaces in the case that the underlying fully nonlinear PDE that governs these surfaces is elliptic or hyperbolic.
