论文标题
欧几里得空间中submanifolds的steklov特征值的上限
Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index
论文作者
论文摘要
我们获得了平滑，紧凑，连接的steklov eigenvalues $σ_k（m）$的上限，$ n $二维的submanifold $ m $ m $ euclidean Space带有边界$σ$，涉及$ m $和$σ$的交叉点Indices $σ$。我们的主要结果之一是根据$σ$的交叉点指数，$σ$的体积和$ m $的体积以及尺寸常数的明确上限。通过考虑$σ$的注射性半径，我们获得了一个上限，相对于Steklov Eigenvalues的渐近学，其最佳指数为$ k \ to \ infty $。
We obtain upper bounds for the Steklov eigenvalues $σ_k(M)$ of a smooth, compact, connected, $n$-dimensional submanifold $M$ of Euclidean space with boundary $Σ$ that involve the intersection indices of $M$ and of $Σ$. One of our main results is an explicit upper bound in terms of the intersection index of $Σ$, the volume of $Σ$ and the volume of $M$ as well as dimensional constants. By also taking the injectivity radius of $Σ$ into account, we obtain an upper bound that has the optimal exponent of $k$ with respect to the asymptotics of the Steklov eigenvalues as $k \to \infty$.
