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| Prescribing Curvature Problems on the Bakry-EmeryRicci Tensor of a Compact Manifold with Boundary? |
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Citation： |
Weimin SHENG,Lixia YUAN.Prescribing Curvature Problems on the Bakry-EmeryRicci Tensor of a Compact Manifold with Boundary?[J].Chinese Annals of Mathematics B,2014,35(1):139~160 |
| Page view： 1784
Net amount： 1864 |
Authors： |
Weimin SHENG; Lixia YUAN; |
Foundation： |
National Natural Science Foundation of China (Nos. 10831008, 11131007). |
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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-Amp`ere 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. |
Keywords： |
k-Curvature, Bakry-Emery Ricci tensor, Complete metric, Dirichletproblem |
Classification： |
53C21, 35J66, 58J50 |
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