Please use this identifier to cite or link to this item: https://doi.org/10.1006/jfan.1998.3271
Title: On Conformal Deformations of Metrics onSn
Authors: Wei, J.
Xu, X. 
Keywords: Conformally invariant operators;Qn-curvature; higher order elliptic differential equations
Issue Date: 1-Aug-1998
Citation: Wei, J., Xu, X. (1998-08-01). On Conformal Deformations of Metrics onSn. Journal of Functional Analysis 157 (1) : 292-325. ScholarBank@NUS Repository. https://doi.org/10.1006/jfan.1998.3271
Abstract: OnSn, there is a naturally metric definednth order conformal invariant operatorPn. Associated with this operator is a so-calledQ-curvature quantity. When two metrics are pointwise conformally related, their associated operators, together with theirQ-curvatures, satisfy the natural differential equations. This paper is devoted to the question of which function can be aQ-curvature candidate. This is the so-calledprescribing Q-curvature problem. Our main result is that ifQis positive, nondegenerate and the naturally defined mapping associated withQhas nonzero degree, then our problem has a solution. This is the natural generalization of prescribing Gaussian curvature onS2intoSn. © 1998 Academic Press.
Source Title: Journal of Functional Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/103695
ISSN: 00221236
DOI: 10.1006/jfan.1998.3271
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