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Alexander Logunov, Nodal sets of Laplace eigenfunctions: polynomial upper est imates of the Hausdorff measure , Ann · 2018

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Isoperimetric relations between Dirichlet and Neumann eigenvalues

math.AP · 2019-06-24 · unverdicted · novelty 5.0

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 math.AP · 2019-06-24 · unverdicted · none · ref 22

    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.