A lower bound for the nodal sets of Steklov eigenfunctions

作者：Wang Xing^*; Zhu Jiuyi

来源：Mathematical Research Letters, 2015, 22(4): 1243-1253.

DOI：10.4310/mrl.2015.v22.n4.a14

• Nodal sets
• Lower bound
• Dirichlet-to-Neumann map
• Steklov eigenfunctions

We consider the lower bound of nodal sets of Steklov eigenfunctions on smooth Riemannian manifolds with boundary-the eigenfunctions of the Dirichlet-to-Neumann map. Let N-lambda be its nodal set. Assume that zero is a regular value of Steklov eigenfunctions. We show that
Hn-1(N-lambda) >= C lambda(3-n/2)
for some positive constant C depending only on the manifold.

• 出版日期2015