论文标题
$ \ mathbb {r}^3 $中规定的高斯曲率的旋转表面
Rotational surfaces of prescribed Gauss curvature in $\mathbb{R}^3$
论文作者
论文摘要
我们研究欧几里德三个空间中的旋转表面，其高斯曲率作为其高斯图的规定函数。通过相位平面分析和在规定功能的轻度假设下，我们概括了恒定高斯曲率的旋转表面的分类。展示在恒定高斯曲率情况下不存在的例子；并分析严格凸图的渐近行为。我们还证明存在奇异径向溶液的存在，使旋转轴正交相交。
We study rotational surfaces in Euclidean 3-space whose Gauss curvature is given as a prescribed function of its Gauss map. By means of a phase plane analysis and under mild assumptions on the prescribed function, we generalize the classification of rotational surfaces of constant Gauss curvature; exhibit examples that cannot exist in the constant Gauss curvature case; and analyze the asymptotic behavior of strictly convex graphs. We also prove the existence of singular radial solutions intersecting orthogonally the axis of rotation.
