On the Chen-Lin Conjecture for the Prescribed Scalar Curvature Problem

被引：2
作者：
Chtioui, Hichem [1 ]
机构：
[1] Sfax Univ, Fac Sci Sfax, Sfax 3018, Tunisia
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 09期
关键词：
Scalar curvature; Nonlinear PDEs; Variational method; Loss of compactness; Critical points at infinity; N PART 1; CONFORMAL DEFORMATION; S-N; METRICS; EXISTENCE; EQUATIONS;
D O I：
10.1007/s12220-023-01362-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a criterion of existence of solutions conjectured by Chen and Lin (J Differ Geom 57:67-171, 2001) for the prescribed scalar curvature problem on the standard n-dimensional sphere, n = 3.
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页数：50
相关论文
共 41 条
[1]   Conformal metrics of prescribed scalar curvature on 4-manifolds: the degree zero case [J].
Ahmedou M. ;
Chtioui H. .
Arabian Journal of Mathematics, 2017, 6 (3) :127-136
[2]  
[Anonymous], 1991, DIFFERENTIAL GEOMETR
[3]  
AUBIN T, 1976, J MATH PURE APPL, V55, P269
[4]   Topological hypothesis for the prescribed scalar curvature problem [J].
Aubin, T ;
Bahri, A .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (10) :843-850
[5]   ON A NONLINEAR ELLIPTIC EQUATION INVOLVING THE CRITICAL SOBOLEV EXPONENT - THE EFFECT OF THE TOPOLOGY OF THE DOMAIN [J].
BAHRI, A ;
CORON, JM .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (03) :253-294
[6]   THE SCALAR-CURVATURE PROBLEM ON THE STANDARD 3-DIMENSIONAL SPHERE [J].
BAHRI, A ;
CORON, JM .
JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 95 (01) :106-172
[7]   An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension [J].
Bahri, A .
DUKE MATHEMATICAL JOURNAL, 1996, 81 (02) :323-466
[8]  
Bahri A., 1989, Pitman Research Notes in Mathematics Series, V182
[9]  
Bahri A., 1991, ANN I H POINCARE-AN, V8, P561, DOI [10.1016/s0294-1449(16)30252-9, DOI 10.1016/S0294-1449(16)30252-9]
[10]  
Ben Ayed M., 2003, ANN IHP, V2003, P543
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