Establishes analytic bounds on nested nodal loops for eigenfunction sums, proves sharpness by smooth counterexample, and constructs biharmonic nodal sets disproving an old conjecture.
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Nested nodal loops for sums of Laplace eigenfunctions
Establishes analytic bounds on nested nodal loops for eigenfunction sums, proves sharpness by smooth counterexample, and constructs biharmonic nodal sets disproving an old conjecture.