Authors conjecture that the count of Neumann eigenvalues ≤ first Dirichlet eigenvalue is governed by the domain's isoperimetric ratio, backed by analysis and numerics, with applications to nodal deficiency and Yau's nodal set conjecture.
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Isoperimetric relations between Dirichlet and Neumann eigenvalues
Authors conjecture that the count of Neumann eigenvalues ≤ first Dirichlet eigenvalue is governed by the domain's isoperimetric ratio, backed by analysis and numerics, with applications to nodal deficiency and Yau's nodal set conjecture.