Slicing surfaces and Fourier restriction conjecture

2008/04/23 by Fabio Nicola, Nicola, Fabio
Mathematics · #42B10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0804.3696

openalex publication_date 2008/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid, the elliptic hyperboloid in ℝⁿ implies that for the cone in ℝⁿ⁺¹. We also prove a new restriction estimate for any surface in ℝ³ locally isometric to the plane and of finite type.

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