scholarly journals A Fourier restriction estimate for surfaces of positive curvature in $\mathbb{R}^6$

2014 ◽  
Vol 30 (3) ◽  
pp. 1015-10136 ◽  
Author(s):  
Faruk Temur
Keyword(s):  
Positive Curvature ◽  
Fourier Restriction ◽  
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.

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.

scholarly journals Slicing surfaces and the Fourier restriction conjecture

2009 ◽  
Vol 52 (2) ◽  
pp. 515-527 ◽  
Author(s):  
Fabio Nicola
Keyword(s):  
Fourier Transform ◽  
Finite Type ◽  
Fourier Restriction ◽  
The Fourier Transform ◽  
Restriction Estimate

AbstractWe deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid and 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.

Biophysics (and sociology) of ceramides.

2005 ◽  
Vol 72 ◽  
pp. 177-188 ◽  
Author(s):  
Félix M. Goñi ◽  
F-Xabier Contreras ◽  
L-Ruth Montes ◽  
Jesús Sot ◽  
Alicia Alonso
Keyword(s):  
Cell Biology ◽  
Positive Curvature ◽  
Acyl Chain ◽  
Cell Signalling ◽  
Hexagonal Structure ◽  
Lipid Monolayer ◽  
Flip Flop ◽  
Long Chain ◽  
Bilayer Permeability

In the past decade, the long-neglected ceramides (N-acylsphingosines) have become one of the most attractive lipid molecules in molecular cell biology, because of their involvement in essential structures (stratum corneum) and processes (cell signalling). Most natural ceramides have a long (16-24 C atoms) N-acyl chain, but short N-acyl chain ceramides (two to six C atoms) also exist in Nature, apart from being extensively used in experimentation, because they can be dispersed easily in water. Long-chain ceramides are among the most hydrophobic molecules in Nature, they are totally insoluble in water and they hardly mix with phospholipids in membranes, giving rise to ceramide-enriched domains. In situ enzymic generation, or external addition, of long-chain ceramides in membranes has at least three important effects: (i) the lipid monolayer tendency to adopt a negative curvature, e.g. through a transition to an inverted hexagonal structure, is increased, (ii) bilayer permeability to aqueous solutes is notoriously enhanced, and (iii) transbilayer (flip-flop) lipid motion is promoted. Short-chain ceramides mix much better with phospholipids, promote a positive curvature in lipid monolayers, and their capacities to increase bilayer permeability or transbilayer motion are very low or non-existent.

On Complete Open Manifolds of Positive Curvature

1969 ◽  
Vol 90 (1) ◽  
pp. 75 ◽  
Author(s):  
Detlef Gromoll ◽  
Wolfgang Meyer
Keyword(s):  
Positive Curvature ◽  
Open Manifolds
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