Yau's conjecture on infinitely many minimal surfaces
Let be a closed three-dimensional manifold. Yau's conjecture. contains infinitely many immersed minimal surfaces. This conjecture has been resolved: Song proved the assertion in full generality, following earlier results for generic metrics and special classes of non-generic metrics.
References
Primary source
Xingzhe Li and Tongrui Wang, “Infinite existence of equivariant minimal hypersurfaces”, arXiv:2604.13422 (2026).
Additional references
8 papers in this index state this conjecture (2014–2026). The statement above is taken from the most recent of them; the others are arXiv:2601.09884, arXiv:2309.09527, arXiv:2007.06004, arXiv:2001.04674, arXiv:1905.07120, arXiv:1901.08440, arXiv:1409.7537.
Progress summary
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