论文标题
Minkowsky规范空间中高空曲面的稳定性
Stability of Hypersurfaces in Minkowsky Normed Spaces
论文作者
论文摘要
我们扩展到Minkowski空间Barbosa和Do Carmo [1]的经典结果，该结果将欧几里得球作为$ \ Mathbb r^n $的独特紧凑型CMC Hypersurface。更确切地说，如果$ k $是$ \ mathbb r^n $的光滑凸体，带有正高斯曲率，包含其内部的起源，而$ m $是一个沉浸式的超出表面，那么对于$ k $而言，存在明确定义的表面积测量，正常矢量场和正常矢量曲率和$ m $的主曲线。因此，我们介绍了有关正常变化的稳定性概念，并计算了相对于$ k $的第二变化公式。最后，我们表明，如果$ m $是紧凑的，具有恒定的Minkowski曲率并且稳定（相对于$ K $），那么$ m $对于$ \ partial k $是同质的。
We extend to Minkowski spaces the classical result of Barbosa and do Carmo [1] that characterizes the euclidean sphere as the unique compact stable CMC hypersurface of $\mathbb R^n$. More precisely, if $K$ is a smooth convex body in $\mathbb R^n$ with positive Gauss curvature, containing the origin in its interior and $M$ is an immersed hypersurface, there are well defined concepts of surface area measure, normal vector field and principal curvatures of $M$ , with respect to $K$. Thus, we introduce the concept of stability with respect to normal variations and compute the formula of second variation with respect to $K$. Finally we show that if $M$ is compact, has constant mean Minkowski curvature and is stable (with respect to $K$) then $M$ is homothetic to $\partial K$.
