论文标题
steklov eigenfunctions的通用特性
Generic properties of Steklov eigenfunctions
论文作者
论文摘要
令$ m^n $为具有光滑边界的平滑紧凑型歧管。我们表明，对于$ \ bar {m^n} $的通用$ c^k $ metic，带有$ k> n-1 $，nonzero steklov eigenvalues很简单。此外，我们还证明了非稳定的steklov特征函数的定期值零，并且是这种通用度量的边界上的摩尔斯函数。这些结果将Uhlenbeck的Laplacians的著名结果推广到Steklov环境。
Let $M^n$ be a smooth compact manifolds with smooth boundary. We show that for a generic $C^k$ metic on $\bar{M^n}$ with $k>n-1$, the nonzero Steklov eigenvalues are simple. Moreover, we also prove that the non-constant Steklov eigenfunctions have zero as a regular value and are Morse functions on the boundary for such generic metric. These results generalize the celebrated results on Laplacians by Uhlenbeck to the Steklov setting.
