scholarly journals A restriction estimate using polynomial partitioning

2015 ◽  
Vol 29 (2) ◽  
pp. 371-413 ◽  
Author(s):  
Larry Guth
Keyword(s):  
Polynomial Partitioning ◽  
Restriction Estimate

scholarly journals Shallow Packings, Semialgebraic Set Systems, Macbeath Regions, and Polynomial Partitioning

2019 ◽  
Vol 61 (4) ◽  
pp. 756-777
Author(s):  
Kunal Dutta ◽  
Arijit Ghosh ◽  
Bruno Jartoux ◽  
Nabil H. Mustafa
Keyword(s):  
Polynomial Partitioning ◽  
Semialgebraic Set ◽  
Set Systems ◽  
Macbeath Regions

scholarly journals Improved restriction estimate for hyperbolic surfaces inR3

2017 ◽  
Vol 273 (3) ◽  
pp. 917-945 ◽  
Author(s):  
Chu-Hee Cho ◽  
Jungjin Lee
Keyword(s):  
Hyperbolic Surfaces ◽  
Restriction Estimate

A Restriction Theorem for a k-Surface in ℝn

2005 ◽  
Vol 48 (2) ◽  
pp. 260-266 ◽  
Author(s):  
Daniel M. Oberlin
Keyword(s):  
Restriction Theorem ◽  
Fourier Restriction ◽  
Restriction Estimate

AbstractWe establish a sharp Fourier restriction estimate for a measure on a k-surface in ℝn, where n = k(k + 3)/2.

scholarly journals Unit Distances in Three Dimensions

2012 ◽  
Vol 21 (4) ◽  
pp. 597-610 ◽  
Author(s):  
HAIM KAPLAN ◽  
JIŘÍ MATOUŠEK ◽  
ZUZANA SAFERNOVÁ ◽  
MICHA SHARIR
Keyword(s):  
Three Dimensions ◽  
Polynomial Partitioning ◽  
Similar Proof ◽  
Partitioning Technique

We show that the number of unit distances determined bynpoints in ℝ3isO(n3/2), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28].

Reduction to Restriction Estimates near the Principal Root Jet

2016 ◽  
Author(s):  
Isroil A. Ikromov ◽  
Detlef Müller
Keyword(s):  
Newton Polyhedron ◽  
Small Letter ◽  
Fourier Restriction ◽  
Restriction Estimate

This chapter shows that one may reduce the desired Fourier restriction estimate to a piece Ssubscript Greek small letter psi of the surface S lying above a small, “horn-shaped” neighborhood Dsubscript Greek small letter psi of the principal root jet ψ‎, on which ∣x₂ − ψ‎(x₁)∣ ≤ ε‎xᵐ₁. Here, ε‎ > 0 can be chosen as small as one wishes. The proof then provides the opportunity to introduce some of the basic tools which will be applied frequently, such as dyadic domain decompositions, rescaling arguments based on the dilations associated to a given edge of the Newton polyhedron, in combination with Greenleaf's restriction and Littlewood–Paley theory, hence summing the estimates that have been obtained for the dyadic pieces.

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