4 papers
Critical points of second Neumann eigenfunctions on some convex domains in two-dimensional space forms
Haiyun Deng, Xuyong Jiang, Xiaoping Yang
In this paper, we investigate critical points of second Neumann eigenfunctions on convex domains in the two-dimensional space forms. We approach this problem from three complementa…
Critical points of the second Neumann eigenfunctions on the quadrangles with symmetry
Haiyun Deng, Changfeng Gui, Xuyong Jiang +3
In this paper, we focus primarily on the symmetry properties of the second Neumann eigenfunction with respect to the symmetry axis or symmetry center of the relevant domain …
Measure upper bounds of nodal sets of solutions to Dirichlet problem of Schrödinger equations
Hairong Liu, Long Tian, Xiaoping Yang
In this paper, we focus on estimating measure upper bounds of nodal sets of solutions to the following boundary value problem \begin{equation*} \left\{ \begin{array}{lll} Îu+Vu=0\…
The Sharp Measure Upper Bound of the Nodal Sets of Neumann Laplace Eigenfunctions on C1,1 Domains
Xiujin Chen, Xiaoping Yang
Let Ω be a bounded domain in R^n with C^{1,1} boundary and let u_λ be a Neumann Laplace eigenfunction in Ω with eigenvalue λ. We show that the (n - 1)-dimensional Hausdorff mea…