Critical local smoothing for the three-dimensional wave equation
We prove the critical L 3 local smoothing estimate for the wave equation in three spatial dimensions, with every positive Sobolev loss. This resolves Sogge's Euclidean local smoothing conjecture in dimension three.
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The square function estimate for the cone in four dimensionsarXiv.orgFaruk TemurOct 8, 2026in the index
We obtain the $L^3$ reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September 2026 OpenAI manuscript. We state these inputs, together with the plate maximal theorem of Di Plinio and Parissis, in a…