Prescribing Curvature Problems on the Bakry-Emery Ricci Tensor of a Compact Manifold with Boundary |
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Authors: | Weimin SHENG and Lixia YUAN |
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Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China 2. Department of Mathematics, Xinjiang Normal University, Urumqi, 830054, China
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Abstract: | The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with boundary to a prescribed function. A consequence of our main result is that there exists a complete metric such that the Monge-Ampère type equation with respect to its Bakry-Emery Ricci tensor is solvable, provided that the initial Bakry-Emery Ricci tensor belongs to a negative convex cone. |
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Keywords: | k-Curvature Bakry-Emery Ricci tensor Complete metric Dirichletproblem |
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