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arxiv: 1711.09423 · v4 · pith:T6PBYRN5new · submitted 2017-11-26 · 🧮 math.DG · math.MG

Bipolar comparison

Nina Lebedeva , Anton Petrunin , Vladimir Zolotov This is my paper
classification 🧮 math.DG math.MG
keywords comparisonalexandrovbipolarcalledconditionconnectionscontinuitydefine
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We define a new type of metric comparison similar to the comparison of Alexandrov. We show that it has strong connections to continuity of optimal transport between regular measures on a Riemannian manifold, in particular to the so called MTW condition introduced by Xi-Nan Ma, Neil Trudinger and Xu-Jia Wang.

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