Non-compactness of the prescribed Q-curvature problem in large dimensions

Juncheng Wei; Chunyi Zhao

doi:10.1007/s00526-011-0477-9

Non-compactness of the prescribed Q-curvature problem in large dimensions

Juncheng Wei^*
, Chunyi Zhao

^*此作品的通讯作者

数学科学学院

Chinese University of Hong Kong

科研成果: 期刊稿件 › 文章 › 同行评审

25 引用（Scopus）

摘要

Let (M, g) be a compact Riemannian manifold of dimension N ≥ 5 and Q_g be its Q curvature. The prescribed Q curvature problem is concerned with finding metric of constant Q curvature in the conformal class of g. This amounts to finding a positive solution to P_g(u) = cu^N+4/N-4, u>0 on M where P_g is the Paneitz operator. We show that for dimensions N ≥ 25, the set of all positive solutions to the prescribed Q curvature problem is non-compact.

源语言	英语
页（从-至）	123-164
页数	42
期刊	Calculus of Variations and Partial Differential Equations
卷	46
期	1-2
DOI	https://doi.org/10.1007/s00526-011-0477-9
出版状态	已出版 - 1月 2013

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AB - Let (M, g) be a compact Riemannian manifold of dimension N ≥ 5 and Qg be its Q curvature. The prescribed Q curvature problem is concerned with finding metric of constant Q curvature in the conformal class of g. This amounts to finding a positive solution to Pg(u) = cuN+4/N-4, u>0 on M where Pg is the Paneitz operator. We show that for dimensions N ≥ 25, the set of all positive solutions to the prescribed Q curvature problem is non-compact.

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Non-compactness of the prescribed Q-curvature problem in large dimensions

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