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

Geometry â—˝  
10.1155/2014/582367 â—˝  
2014 â—˝  
Vol 2014 â—˝  
pp. 1-9
Author(s):  
Ridha Yacoub
Keyword(s):  
Scalar Curvature â—˝  
Critical Points â—˝  
Mean Curvature â—˝  
Existence Results â—˝  
Curvature Condition â—˝  
Multiplicity Results â—˝  
3 Dimensional â—˝  
Existence And Multiplicity â—˝  
Curvature Problem â—˝  
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

Open Mathematics â—˝  
2014 â—˝  
Vol 12 (12) â—˝  
Author(s):  
Dina Abuzaid â—˝  
Randa Ben Mahmoud â—˝  
Hichem Chtioui â—˝  
Afef Rigane
Keyword(s):  
Scalar Curvature â—˝  
Conformal Metrics â—˝  
Standard Sphere â—˝  
Multiplicity Results â—˝  
Existence And Multiplicity â—˝  
Hopf Formula â—˝  
Curvature Problem â—˝  
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 Existence and Multiplicity Results for the Prescribed Webster Scalar Curvature Problem on Three CR Manifolds

2011 â—˝  
Vol 23 (2) â—˝  
pp. 878-894 â—˝  
Author(s):  
Hichem Chtioui â—˝  
Mohameden Ould Ahmedou â—˝  
Ridha Yacoub
Keyword(s):  
Scalar Curvature â—˝  
Cr Manifolds â—˝  
Multiplicity Results â—˝  
Existence And Multiplicity â—˝  
Webster Scalar Curvature â—˝  
Curvature Problem

Topological Methods for Boundary Mean Curvature Problem on Bn

2014 â—˝  
Vol 14 (2) â—˝  
Author(s):  
Mohammed Ali Al-Ghamdi â—˝  
Hichem Chtioui â—˝  
Khadijah Sharaf
Keyword(s):  
Critical Points â—˝  
Mean Curvature â—˝  
Topological Method â—˝  
Topological Methods â—˝  
Critical Points At Infinity â—˝  
The Mean â—˝  
Curvature Problem â—˝  
Boundary Mean Curvature

AbstractUsing an algebraic topological method and the tools of the theory of the critical points at infinity, we provide a variety of classes of functions that can be realized as the mean curvature on the boundary of the the n-dimensional balls.

scholarly journals The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds

2019 â—˝  
Vol 358 â—˝  
pp. 106854 â—˝  
Author(s):  
Xuezhang Chen â—˝  
Yuping Ruan â—˝  
Liming Sun
Keyword(s):  
Scalar Curvature â—˝  
Mean Curvature â—˝  
Constant Scalar Curvature â—˝  
Compact Manifolds â—˝  
Curvature Problem â—˝  
Boundary Mean Curvature

scholarly journals On far-outlying constant mean curvature spheres in asymptotically flat Riemannian 3-manifolds

2020 â—˝  
Vol 2020 (767) â—˝  
pp. 161-191
Author(s):  
Otis Chodosh â—˝  
Michael Eichmair
Keyword(s):  
Scalar Curvature â—˝  
Mean Curvature â—˝  
Constant Mean Curvature â—˝  
Existence Results â—˝  
Asymptotically Flat â—˝  
Weingarten Surfaces â—˝  
Differential Geom

AbstractWe extend the Lyapunov–Schmidt analysis of outlying stable constant mean curvature spheres in the work of S. Brendle and the second-named author [S. Brendle and M. Eichmair, Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94 2013, 3, 387–407] to the “far-off-center” regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable constant mean curvature spheres that depend delicately on the behavior of scalar curvature at infinity.

scholarly journals Existence and multiplicity results for a Steklov problem involving (p(x), q(x))-Laplacian operator

2021 â—˝  
Vol 0 (0) â—˝  
Author(s):  
Belhadj Karim â—˝  
A. Lakhdi â—˝  
M. R. Sidi Ammi â—˝  
A. Zerouali
Keyword(s):  
Critical Points â—˝  
Elliptic Problem â—˝  
Laplacian Operator â—˝  
Three Solutions â—˝  
Multiplicity Results â—˝  
Steklov Problem â—˝  
Three Critical Points Theorem â—˝  
Existence And Multiplicity

Abstract In this work, we are concerned with a generalized Steklov problem with (p(x), q(x))-Laplacian operator. Under some appropriate conditions on the data involved in the elliptic problem, we prove the existence of at least three solutions using Ricceri’s three critical points theorem.

scholarly journals A Morse theoretical approach for the boundary mean curvature problem on B4

2008 â—˝  
Vol 254 (5) â—˝  
pp. 1307-1341 â—˝  
Author(s):  
Wael Abdelhedi â—˝  
Hichem Chtioui â—˝  
Mohameden Ould Ahmedou
Keyword(s):  
Theoretical Approach â—˝  
Mean Curvature â—˝  
Curvature Problem â—˝  
Boundary Mean Curvature

Prescribing the Scalar Curvature Problem on Three and Four Manifolds

2003 â—˝  
Vol 3 (4) â—˝  
Author(s):  
Hichem Chtioui
Keyword(s):  
Scalar Curvature â—˝  
Riemannian Manifolds â—˝  
Critical Points â—˝  
New Class â—˝  
Critical Points At Infinity â—˝  
Four Manifolds â—˝  
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.

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