scholarly journals $\sup \times \inf$ Inequalities for the Scalar Curvature Equation in Dimensions 4 and 5

2022 ◽  
Vol 38 (1) ◽  
pp. 92-110
Author(s):  
global sci
Keyword(s):  
Scalar Curvature ◽  
Curvature Equation

On positive entire solutions of the elliptic equation Δu + K(x)up = 0 and its applications to Riemannian geometry

1996 ◽  
Vol 126 (2) ◽  
pp. 225-237 ◽  
Author(s):  
Changfeng Gui
Keyword(s):  
Elliptic Equation ◽  
Asymptotic Behaviour ◽  
Scalar Curvature ◽  
Riemannian Geometry ◽  
Semilinear Elliptic Equation ◽  
Entire Space ◽  
Entire Solutions ◽  
Curvature Equation ◽  
Semilinear Elliptic ◽  
Special Case

We study the existence and asymptotic behaviour of positive solutions of a semilinear elliptic equation in entire space. A special case of this equation is the scalar curvature equation which arises in Riemannian geometry.

scholarly journals Multiplicity results for the scalar curvature equation

2015 ◽  
Vol 259 (8) ◽  
pp. 4327-4355 ◽  
Author(s):  
Isabel Flores ◽  
Matteo Franca
Keyword(s):  
Scalar Curvature ◽  
Multiplicity Results ◽  
Curvature Equation

CONSTRUCTION OF BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON Sn I: UNIFORM CANCELLATION

2012 ◽  
Vol 14 (02) ◽  
pp. 1250008 ◽  
Author(s):  
MAN CHUN LEUNG
Keyword(s):  
Scalar Curvature ◽  
Positive Solutions ◽  
Infinite Number ◽  
Reduction Method ◽  
Blow Up ◽  
Curvature Function ◽  
Cancellation Property ◽  
First Order ◽  
Curvature Equation ◽  
Derivatives Of

For n ≥ 6, using the Lyapunov–Schmidt reduction method, we describe how to construct (scalar curvature) functions on Sn, so that each of them enables the conformal scalar curvature equation to have an infinite number of positive solutions, which form a blow-up sequence. The prescribed scalar curvature function is shown to have Cn - 1,β smoothness. We present the argument in two parts. In this first part, we discuss the uniform cancellation property in the Lyapunov–Schmidt reduction method for the scalar curvature equation. We also explore relation between the Kazdan–Warner condition and the first-order derivatives of the reduced functional, and symmetry in the second-order derivatives of the reduced functional.

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