Year: 2026
Type: preprint
Abstract: In this work, we establish the sharp $L^2 \to L^4$ extension inequality for a large class of quadratic surfaces in $\mathbb{F}^3$, where $\mathbb{F}$ is a finite field of odd characteristic. These surfaces include the cones without the origin and the spheres with nonzero radius $j$ such that $-j$ is not a square in $\mathbb{F}$. We also show that the maximizers of these inequalities must have constant modulus.
Source: arXiv (Cornell University)
Author: Ronda, Pedro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212491563