For each fixed smooth closed connected Riemannian surface, the nodal set of every nonzero real Laplace eigenfunction of eigenvalue λ>0 has length at most C√λ, with C depending on the surface.
For each fixed smooth closed connected Riemannian surface, the nodal set of every nonzero real Laplace eigenfunction of eigenvalue λ>0 has length at most C√λ, with C depending on the surface.
For each fixed smooth closed connected Riemannian surface, the nodal set of every nonzero real Laplace eigenfunction of eigenvalue λ>0 has length at most C√λ, with C depending on the surface.
If correct, proves the missing upper half of Yau’s nodal-length conjecture for smooth closed surfaces.
Is nodal length on every smooth closed surface bounded above by C√λ?
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