论文标题
关于一个处方，几乎恒定曲率的属的紧凑型表面的不存在，接近奇异极限
On the non-existence of compact surfaces of genus one with prescribed, almost constant mean curvature, close to the singular limit
论文作者
论文摘要
在具有笛卡尔参考系统的Euclidean 3空间中，我们考虑了一类称为Delaunay Tori的表面，该表面是由弯曲的Delaunay气缸的弯曲片段，其颈部尺寸$ A $ A $ a $ a $ n $ lobes的围绕着以起源为中心。这样的表面是完整而紧凑的，当$ n $很大时，属的属和几乎是恒定的，例如1平均曲率。考虑一类映射$ h \ colon \ mathbb {r}^{3} \ to \ mathbb {r {r} $，以至于$ h（x）\ 1 $ as $ | | x | x | x | \ t \ to \ to \ to \ to \ to \ to \ infty $ a $ n $ n $ n $ |脖子大小$ a $没有在Delaunay圆环上以普通图构造的参数表面，其平均曲率等于每个点的$ H $。
In Euclidean 3-space endowed with a Cartesian reference system we consider a class of surfaces, called Delaunay tori, constructed by bending segments of Delaunay cylinders with neck-size $a$ and $n$ lobes along circumferences centered at the origin. Such surfaces are complete and compact, have genus one and almost constant, say 1, mean curvature, when $n$ is large. Considering a class of mappings $H\colon\mathbb{R}^{3}\to\mathbb{R}$ such that $H(X)\to 1$ as $|X|\to\infty$ with some decay of inverse-power type, we show that for $n$ large and $|a|$ small, in a suitable neighborhood of any Delaunay torus with $n$ lobes and neck-size $a$ there is no parametric surface constructed as normal graph over the Delaunay torus and whose mean curvature equals $H$ at every point.
