The effect of pinching conditions in prescribing Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Q $$\end{document}-curvature on standard spheres

被引：0

作者：

Mohamed Ben Ayed

Khalil El Mehdi

机构：

[1] Qassim University,Department of Mathematics, College of Science

[2] Université de Sfax,Faculté des Sciences de Sfax

[3] Université de Nouakchott,Faculté des Sciences et Techniques

来源：

Annals of Global Analysis and Geometry | 2023年 / 63卷 / 1期

关键词：

Noncompact variational problems; Critical points at infinity; curvature; 35C60; 58J60; 53C21;

D O I：

10.1007/s10455-022-09878-6

中图分类号：

学科分类号：

摘要：

In this paper, we study the problem of prescribing a fourth-order conformal invariant on standard spheres. This problem is variational but it is noncompact due to the presence of nonconverging orbits of the gradient flow, the so called critical points at infinity. Following the method advised by Bahri we determine all such critical points at infinity and compute their contribution to the difference of topology between the level sets of the associated Euler–Lagrange functional. We then derive some existence results under pinching conditions.

引用

共 28 条

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Nonlinear Differential Equations and Applications NoDEA, 2018, 25 (5)
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[28] Four families of projectively flat Finsler metrics with K=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{K}=1$$\end{document} and their non-Riemannian curvature properties
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