Yau's nodal volume conjecture
Yau's nodal volume conjecture
Let be a compact Riemannian manifold without boundary, and let be an eigenfunction satisfying
Write for its nodal volume. Yau's conjecture. There exist constants such that
Thus the nodal volume should be of the order of the corresponding frequency. The source provides no evidence that this conjecture has been resolved in the stated generality.
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Sources & referencesView supporting material
Primary source
Michele Stecconi and Anna Paola Todino, “Statistics on Yau's conjecture: Variance asymptotics”, arXiv:2607.09946 (2026).
Additional references
7 papers in this index state this conjecture (2011–2026). The statement above is taken from the most recent of them; the others are arXiv:2512.12305, arXiv:2508.07861, arXiv:1512.06818, arXiv:1408.7101, arXiv:1402.4323, arXiv:1112.4352.
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