|Nov 21, 2023
Guth devised k-broad estimates to improve the restriction conjecture in higher dimensions. Following his arguments Ou and Wang improved the cone restriction estimates as well. Based on their cone restriction estimates Gao, Liu, Miao, and Xi obtained some improved local smoothing estimates for the wave equation in higher dimensions. In this seminar, we will talk about the differences between the cone restriction estimate and the local smoothing estimate, and the difficulties caused by the differences.