Local smoothing conjecture

In harmonic analysis, the local smoothing conjecture is a conjecture about the behavior of solutions to the wave equation. The conjecture was first proposed by Christopher Sogge in 1991. It was proven in the dimension 2 case by Guth, Wang, and Zhang in 2019.

The local smooth conjecture is the strongest in a sequence of conjectures in harmonic analysis. It implies the Bochner-Riesz conjecture, which in turn implies the restriction conjecture, which implies the Kakeya conjecture.


References

  1. ↑ Sogge, Christopher D. (1991). "Propagation of singularities and maximal functions in the plane". Inventiones mathematicae. 104 (1): 349–376. doi:10.1007/BF01245080. ISSN 0020-9910. Retrieved 2026-10-26.
  2. ↑ Guth, Larry; Wang, Hong; Zhang, Ruixiang (2020-09-01). "A sharp square function estimate for the cone in $\mathbb{R}^3$". Annals of Mathematics. 192 (2): 551–581. doi:10.4007/annals.2020.192.2.6. ISSN 0003-486X. Retrieved 2026-10-26.
  3. ↑ Tao, Terence (2024-11-17). "Terence Tao (@tao@mathstodon.xyz)". Mathstodon. Retrieved 2025-07-20.
  4. ↑ Cepelewicz, Jordana (2023-09-12). "A Tower of Conjectures That Rests Upon a Needle". Quanta Magazine. Retrieved 2025-07-20.