Optimal transportation on non-compact manifolds
Optimal transportation on non-compact manifolds
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DOI：
10.1007/s11856-010-0001-5
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发表时间：
2007-11
影响因子：
1
通讯作者：
A. Fathi;A. Figalli
中科院分区：
文献类型：
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作者：
A. Fathi;A. Figalli
在这项工作中，我们展示了如何获得非紧流形的结果，已经做了蒙赫运输问题的成本来自Tonelli拉格朗日紧流形。特别地，对于类型为dr，r> 1的代价的已知结果，其中d是完备黎曼流形的黎曼距离，在没有任何曲率限制的情况下成立。
In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the typedr,r> 1, where d is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.