Busemann functions on the Wasserstein space,Calculus of Variations and Partial Differential Equations

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Busemann functions on the Wasserstein space
Calculus of Variations and Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-04-27 , DOI: 10.1007/s00526-021-01937-3
Guomin Zhu , Wen-Long Li , Xiaojun Cui

We study rays and co-rays in the Wasserstein space \(P_p({\mathcal {X}})\) (\(p > 1\)) whose ambient space \({\mathcal {X}}\) is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability measures concentrated on the set of rays in the ambient space. We show the existence of co-rays for any prescribed initial probability measure. We introduce Busemann functions on the Wasserstein space and show that co-rays are negative gradient lines in some sense.

更新日期：2021-04-27

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