Sharp Estimates for Bubbling Solutions to Some Fourth-Order Geometric Equations

被引:5
作者
Ndiaye, Cheikh Birahim [1 ]
机构
[1] Justus Liebig Univ Giessen, Math Inst, Arndtstr 2, D-35392 Giessen, Germany
关键词
ZETA-FUNCTIONAL DETERMINANTS; NONLINEAR ELLIPTIC-EQUATIONS; CONSTANT Q-CURVATURE; PLUS INF INEQUALITY; CONFORMAL METRICS; MANIFOLDS; EXISTENCE; DEFORMATION; 4-MANIFOLDS; COMPACTNESS;
D O I
10.1093/imrn/rnw007
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article, we derive an analogue of the exact bubbling rate formula of Chen-Lin [19] for the Q-curvature equation on closed four-dimensional Riemannian manifolds. Using this, we derive new existence results for the prescribed Q-curvature problem on closed four-dimensional Riemannian manifolds under a positive mass type assumption. Furthermore, as an other application, we deduce a compactness theorem for conformal metrics with prescribed Q-curvature on closed four-dimensional Riemannian manifolds under a nondegeneracy assumption. Our method is of variational nature and is based on the tools of critical points theory at infinity of Bahri [3]. Our exact bubbling rate formula is also used in a subsequent paper to interpret the index counting formula in [54] as the Leray-Schauder degree of the corresponding equation.
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页码:643 / 676
页数:34
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