5 papers · 1 filter
Quantitative Pólya inequalities for annular sectors
Guowei Dai, Yingxin Sun
We prove explicit positive corrections to the Dirichlet and Neumann Pólya inequalities at every positive eigenvalue index of every annular sector. The coefficients depend only on t…
Pólya's conjecture for Neumann eigenvalues of annuli
Guowei Dai, Yingxin Sun
We prove strict Pólya inequalities for every positive Neumann eigenvalue of every Euclidean annulus. The proof preserves the exact Weyl area term through a radial action identity a…
Sharp Neumann eigenvalue means on triangles
Guowei Dai, Yingxin Sun
We prove two conjectures of Laugesen and Siudeja: the equilateral triangle uniquely maximizes the harmonic mean of the first two positive Neumann eigenvalues at fixed perimeter and…
Neumann eigenvalues of isosceles triangles: monotonicity and asymptotics
Guowei Dai, Yingxin Sun, Yong Zhang
We prove Laugesen and Siudeja's conjecture on Neumann eigenvalues of isosceles triangles. After multiplication by the squared diameter, the first positive symmetric eigenvalue incr…
Robin eigenvalue ratios: monotonicity on boxes and counterexamples
Guowei Dai, Yingxin Sun
We disprove Laugesen's conjecture that the ratio of the first two Robin eigenvalues decreases with the positive boundary parameter. On any prescribed compact interval of positive p…