A sharp bilinear restriction estimate for paraboloids

2002/10/07 by Terence Tao, Tao, Terence · 2 citations
Mathematics · #35Q55 #42B15 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CA #msc:35Q55 #msc:42B15

paper · pdf · doi:10.48550/arxiv.math/0210084

21 pages, no figures, to appear, GAFA. More explanation added and some minor typos removed

openalex publication_date 2002/10/07 · arxiv created 2002/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Wolff obtained a sharp L² bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of ``elliptic surfaces'' such as paraboloids and spheres. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon the known restriction theory for the paraboloid and sphere.

Citations

• From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE
• Space‐time estimates for null forms and the local existence theorem

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