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<p>We consider the prescribed Q-curvature problem on closed Riemannian manifolds <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M^n,g_0)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( n\ge 5\)</EquationSource> </InlineEquation>. It is a non-compact variational problem. A complete study of the lack of compactness has been established in dimensions 5, 6 and 7 in [<CitationRef CitationID="CR2">2</CitationRef>] and [<CitationRef CitationID="CR3">3</CitationRef>]. In this paper we deal with the problem in dimensions <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( n\ge 7\)</EquationSource> </InlineEquation>. Under a non-degeneracy hypothesis on the prescribed function, we provide a full description of the lack of compactness of the problem and topological conditions to ensure existence results.</p>

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Higher dimensional Q-curvature problems on Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年10月11日

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  • Mohammed Ali Mohammed Alghamdi,
  • Hichem Chtioui,
  • Gdarat Mohamed

摘要

We consider the prescribed Q-curvature problem on closed Riemannian manifolds \((M^n,g_0)\) , \( n\ge 5\) . It is a non-compact variational problem. A complete study of the lack of compactness has been established in dimensions 5, 6 and 7 in [2] and [3]. In this paper we deal with the problem in dimensions \( n\ge 7\) . Under a non-degeneracy hypothesis on the prescribed function, we provide a full description of the lack of compactness of the problem and topological conditions to ensure existence results.