Second Order Analysis on (P2(m), W2)
Second Order Analysis on (P2(m), W2)
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(P2(m), W2) 的二阶分析
DOI：
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发表时间：
2012
期刊：
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通讯作者：
N. Gigli
中科院分区：
文献类型：
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作者：
N. Gigli
本文对具有二次最优迁移距离W_2的黎曼流形上的概率测度空间进行了严格的二阶分析。讨论内容包括：协变导数的定义，平行迁移存在性问题的讨论，黎曼曲率张量的微积分，指数映射的可微性和Jacobi场的存在性。这种方法不需要对所考虑的措施进行任何平滑假设。
The author develops a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. The discussion includes: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Jacobi fields. This approach does not require any smoothness assumption on the measures considered.