Cone restriction via direction-restricted two-ends Furstenberg estimates

Abstract

We investigate a direct two-ends approach to restriction for the truncated cone in ${\mathbb{R}}^n$, which gives the diagonal restriction range \[ p>2+\frac{4(7n+15)}{11n^2-n-24},\qquad n\ge10. \] This improves the range obtained by applying the result of Wang--Wu and then slicing.