Restriction estimates for certain surfaces of finite type in ${\mathbb{R}}^3$

Abstract

In this paper, we study the restriction estimate for a certain surface of finite type in ${\mathbb{R}}^3$, and partially improves the results of Buschenhenke-Müller-Vargas. The key ingredients of the proof include the so called generalized rescaling technique based on a decomposition adapted to finite type geometry, a decoupling inequality and reduction of dimension arguments.

22 pages

References in corpus (2)

• A Fourier Restriction Theorem For A Twodimensional Surface Of Finite Type
• Uniform $l^2$-decoupling in ${\mathbb{R}}^2$ for Polynomials