论文标题
稳定的毛细血管高空曲面和径向重量的球中的分区问题
Stable capillary hypersurfaces and the partitioning problem in balls with radial weights
论文作者
论文摘要
在一个圆球$ b \ subset \ mathbb {r}^{n+1} $中，带有$ o（n+1）$ - 不变度度量，我们考虑了一个重量和区域的径向函数。我们证明，$ b $中的紧凑型双面超脸，这在加权意义上是稳定的毛细血管，并且对一条包含$ b $的中心的一线对称是同型$ n $二维磁盘。当与hsiang对称和其他稳定性结果结合使用时，可以推断出高斯重量$ b $中任何等等区域的内部边界是革命的$ n $ disk。对于$ n = 2 $，我们还表明，在$ b $ of属0的$ b $中，紧凑的加权稳定毛细管表面是革命的封闭磁盘。
In a round ball $B\subset\mathbb{R}^{n+1}$ endowed with an $O(n+1)$-invariant metric we consider a radial function that weights volume and area. We prove that a compact two-sided hypersurface in $B$ which is stable capillary in weighted sense and symmetric about some line containing the center of $B$ is homeomorphic to a closed $n$-dimensional disk. When combined with Hsiang symmetrization and other stability results this allows to deduce that the interior boundary of any isoperimetric region in $B$ for the Gaussian weight is a closed $n$-disk of revolution. For $n=2$ we also show that a compact weighted stable capillary surface in $B$ of genus 0 is a closed disk of revolution.
