Prescribing curvature problem of Bakry-mery Ricci tensor

Prescribing curvature problem of Bakry-mery Ricci tensor

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摘要 We consider the problem of deforming a metric in its conformal class on a closed manifold, such that the k-curvature defined by the Bakry-mery Ricci tensor is a constant. We show its solvability on the manifold, provided that the initial Bakry-mery Ricci tensor belongs to a negative cone. Moveover, the Monge-Ampère type equation with respect to the Bakry-mery Ricci tensor is also considered. We consider the problem of deforming a metric in its conformal class on a closed manifold, such that the k-curvature defined by the Bakry-mery Ricci tensor is a constant. We show its solvability on the manifold, provided that the initial Bakry-mery Ricci tensor belongs to a negative cone. Moveover, the Monge-Ampère type equation with respect to the Bakry-mery Ricci tensor is also considered.

作者 YUAN LiXia

机构地区 Department of Mathematics Department of Mathematics

出处《Science China Mathematics》 SCIE 2013年第9期1935-1944,共10页 中国科学：数学（英文版）

关键词 Bakry-émery Ricci tensor k-curvature 张量曲率处方梅市场变化放大器歧管

分类号 O186.12 [理学—基础数学]

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Science China Mathematics

2013年第9期

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Prescribing curvature problem of Bakry-mery Ricci tensor

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