Generic properties of Steklov eigenfunctions

2022/06/29 by Wang, Lihan
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.14385

Abstract

Let Mⁿ be a smooth compact manifolds with smooth boundary. We show that for a generic C^k metic on Mⁿ 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.

Related

• On the critical points of Steklov eigenfunctions
• Generic properties of discrete Steklov eigenfunctions
• Generic metrics, eigenfunctions and riemannian coverings of non compact manifolds
• A lower bound for the nodal sets of Steklov eigenfunctions
• Doubling property and vanishing order of Steklov eigenfunctions