β-flatness condition in CR spheres multiplicity results

2020 ◽  
Vol 31 (03) ◽  
pp. 2050023
Author(s):  
Najoua Gamara ◽  
Boutheina Hafassa ◽  
Akrem Makni
Keyword(s):  
Lower Bound ◽  
Scalar Curvature ◽  
Critical Points ◽  
Number Of Solutions ◽  
Multiplicity Results ◽  
Type Formula ◽  
Critical Points At Infinity ◽  
Cauchy Riemann

We give multiplicity results for the problem of prescribing the scalar curvature on Cauchy–Riemann spheres under [Formula: see text]-flatness condition. To find a lower bound for the number of solutions, we use Bahri’s methods based on the theory of critical points at infinity and a Poincaré–Hopf-type formula.

Prescribing the Scalar Curvature Problem on Three and Four Manifolds

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Hichem Chtioui
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Critical Points ◽  
New Class ◽  
Critical Points At Infinity ◽  
Four Manifolds ◽  
Curvature Problem

AbstractThis paper is devoted to the prescribed scalar curvature problem on 3 and 4- dimensional Riemannian manifolds. We give a new class of functionals which can be realized as scalar curvature. Our proof uses topological arguments and the tools of the theory of the critical points at infinity.

scholarly journals Prescribing scalar curvatures: non compactness versus critical points at infinity

2019 ◽  
Vol 4 (1) ◽  
pp. 51-82 ◽  
Author(s):  
Martin Mayer
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Critical Points ◽  
Gradient Flow ◽  
Slight Modification ◽  
Positive Function ◽  
Flow Lines ◽  
Critical Points At Infinity

Abstract We illustrate an example of a generic, positive function K on a Riemannian manifold to be conformally prescribed as the scalar curvature, for which the corresponding Yamabe type L2-gradient flow exhibits non compact flow lines, while a slight modification of it is compact.

scholarly journals Prescribing the Scalar Curvature under Minimal Boundary Conditions on the Half Sphere

2002 ◽  
Vol 2 (2) ◽  
Author(s):  
Mohamed Ben Ayed ◽  
Khalil El Mehdi ◽  
Mohameden Ould Ahmedou
Keyword(s):  
Boundary Conditions ◽  
Variational Problem ◽  
Scalar Curvature ◽  
Critical Points ◽  
Existence Results ◽  
Topological Methods ◽  
Critical Points At Infinity

AbstractThis paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results on the standard half sphere.

scholarly journals Existence and Multiplicity Results for the Scalar Curvature Problem on the Half-Sphere 𝕊+3

Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ridha Yacoub
Keyword(s):  
Scalar Curvature ◽  
Critical Points ◽  
Mean Curvature ◽  
Existence Results ◽  
Curvature Condition ◽  
Multiplicity Results ◽  
3 Dimensional ◽  
Existence And Multiplicity ◽  
Curvature Problem ◽  
Boundary Mean Curvature

In this paper we deal with the scalar curvature problem under minimal boundary mean curvature condition on the standard 3-dimensional half-sphere. Using tools related to the theory of critical points at infinity, we give existence results under perturbative and nonperturbative hypothesis, and with the help of some “Morse inequalities at infinity”, we provide multiplicity results for our problem.

Topological tools for the prescribed scalar curvature problem on S n

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Dina Abuzaid ◽  
Randa Ben Mahmoud ◽  
Hichem Chtioui ◽  
Afef Rigane
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Standard Sphere ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Hopf Formula ◽  
Curvature Problem ◽  
Formula Type

AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

Sign in / Sign up

Export Citation Format

Share Document