The reciprocal-sum deficit for the first d nonzero Neumann eigenvalues controls eigenvalue displacements, spectral splitting, and Fraenkel asymmetry with sharp, optimal exponents.
Ashbaugh and Rafael D
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Spectral and Geometric Stability for the Reciprocal Sum of Neumann Eigenvalues
The reciprocal-sum deficit for the first d nonzero Neumann eigenvalues controls eigenvalue displacements, spectral splitting, and Fraenkel asymmetry with sharp, optimal exponents.