On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid

2021 ◽  
pp. 193-222
Author(s):  
Stefan Buschenhenke ◽  
Detlef Müller ◽  
Ana Vargas
Keyword(s):  
Finite Type ◽  
Hyperbolic Paraboloid ◽  
Fourier Restriction

Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

2014 ◽  
Keyword(s):  
Harmonic Analysis ◽  
Finite Type ◽  
Maximal Function ◽  
Oscillatory Integrals ◽  
The Other ◽  
Riemannian Surface ◽  
Fourier Restriction ◽  
Newton Polyhedra ◽  
The Given ◽  
Finite Type Hypersurfaces

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a smooth, finite type hypersurface in R³ with Riemannian surface measure dσ‎). The first problem is a classical question about estimates for oscillatory integrals, and there exists a huge body of results on it, in particular for convex hypersurfaces. The other two problems had first been formulated by Stein: the study of maximal averages along hypersurfaces has been initiated in Stein's work on the spherical maximal function, and also the idea of Fourier restriction goes back to him.

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.

scholarly journals A Fourier restriction theorem for a perturbed hyperbolic paraboloid

2019 ◽  
Vol 120 (1) ◽  
pp. 124-154
Author(s):  
Stefan Buschenhenke ◽  
Detlef Müller ◽  
Ana Vargas
Keyword(s):  
Hyperbolic Paraboloid ◽  
Restriction Theorem ◽  
Fourier Restriction

scholarly journals A Fourier restriction theorem for a two-dimensional surface of finite type

2017 ◽  
Vol 10 (4) ◽  
pp. 817-891 ◽  
Author(s):  
Stefan Buschenhenke ◽  
Detlef Müller ◽  
Ana Vargas
Keyword(s):  
Finite Type ◽  
Two Dimensional ◽  
Restriction Theorem ◽  
Fourier Restriction ◽  
Dimensional Surface

TEST OF A PRESTRESSED CONCRETE HYPERBOLIC PARABOLOID SHELL

PCI Journal ◽  
1958 ◽  
Vol 3 (1) ◽  
pp. 70-78
Author(s):  
T. Y. Lin ◽  
R. Itaya
Keyword(s):  
Prestressed Concrete ◽  
Hyperbolic Paraboloid

Buckling characteristics of cut-out borne composite stiffened hyperbolic paraboloid shell panel

2021 ◽  
pp. 146442072110058
Author(s):  
Sarmila Sahoo
Keyword(s):  
Finite Element ◽  
Orientation Angle ◽  
Buckling Load ◽  
Benchmark Problems ◽  
Hyperbolic Paraboloid ◽  
Element Analysis ◽  
Load Effect ◽  
Global Buckling ◽  
Fiber Orientation Angle ◽  
Shell Panel

The present study investigates buckling characteristics of cut-out borne stiffened hyperbolic paraboloid shell panel made of laminated composites using finite element analysis to evaluate the governing differential equations of global buckling of the structure. The finite element code is validated by solving benchmark problems from literature. Different parametric variations are studied to find the optimum panel buckling load. Laminations, boundary conditions, depth of stiffener and arrangement of stiffeners are found to influence the panel buckling load. Effect of different parameters like cut-out size, shell width to thickness ratio, degree of orthotropy and fiber orientation angle of the composite layers on buckling load are also studied. Parametric and comparative studies are conducted to analyze the buckling strength of composite hyperbolic paraboloid shell panel with cut-out.

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