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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 |
Appears in Collections: | Staff Publications |
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