Generic properties of Steklov eigenfunctions

Wang, Lihan

doi:10.1090/tran/8769

Generic properties of Steklov eigenfunctions
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by Lihan Wang PDF

Trans. Amer. Math. Soc. 375 (2022), 8241-8255 Request permission

Abstract:

Let $M^n$ be a smooth compact manifold with smooth boundary. We show that for a generic $C^k$ metric on ${}\mkern 3mu\overline {\mkern -3muM^n}$ with $k>n-1$, the non-zero Steklov eigenvalues are simple. Moreover, we 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.

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