Complete Conformal Metrics of Negative Ricci Curvature on Euclidean Spaces

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• 作者：Zhenan Sui
• 关键词：Complete conformal metrics ; Ricci curvature ; Supersolution ; Subsolution
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：893-907
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

We show the existence and nonexistence results of complete conformal metrics with prescribed symmetric functions of the eigenvalues of the Ricci tensor defined on negative cones on Euclidean spaces. Our results are sharp under certain decay conditions of the prescribed curvature functions.