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math.DG2026
Isoperimetric bounds for the weighted Neumann and Steklov eigenvalues in dimensions three through six
Daguang Chen, Hao Liu, Chengxi Yang
For , we determine the sharp isoperimetric bound for the mass-normalized first weighted Neumann eigenvalue on bounded Euclidean domains. For every finite nonnegative no…
math.DG2026
Sharp harmonic-mean inequalities for Neumann and Aharonov--Bohm spectra
Daguang Chen, Chengxi Yang
We prove sharp two-eigenvalue isoperimetric inequalities for Neumann and Aharonov--Bohm Neumann spectra on surfaces. If is smooth, simply connected and proper…
math.DG2026
Sharp shifted reciprocal sums of Neumann eigenvalues on space forms
Daguang Chen, Chengxi Yang
Let be the space form of sectional curvature , so that $\mathbb{M}_{-1}^n=\mathbb{H}^n, \mathbb{M}_{0}^n=\mathbb{R}^n, \mathbb{M}_{1}^n=\mathbb{S}^…