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math.AP2026
Near-boundary rigidity and strict maximum modulus for Neumann eigenfunctions on convex planar domains
Haiyun Deng, Xuyong Jiang, Xiaoping Yang
We develop a near-boundary rigidity theorem for arbitrary nonzero Neumann eigenfunctions on bounded convex planar domains. Precisely, if an eigenfunction with positive eigenval…
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
We classify the symmetry and multiplicity of the second Neumann eigenvalue on isosceles trapezoids and kites as the height varies. Precisely, away from a unique transition height,…