3 papers
math.AP2026
Quantitative characterization of deviations from the hot spots conjecture on convex domains in two-dimensional space forms
Haiyun Deng, Xuyong Jiang, Xiaoping Yang
In this paper, we study critical points of second Neumann eigenfunctions on convex domains in two-dimensional space forms from three complementary perspectives: spectral and geomet…
math.AP2026
Symmetry and critical points of second Neumann eigenfunctions on isosceles trapezoids and kites
Haiyun Deng, Changfeng Gui, Xuyong Jiang +3
In this paper, we determine the symmetry properties and non-vertex critical points of the second Neumann eigenfunction , as well as the multiplicity of the corresponding eigenva…
math.AP2024
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 measure…