Bipolar comparison

Abstract

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.

25 pages, 16 figures

Cited by in corpus (7)

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• 5-point CAT(0) spaces after Tetsu Toyoda
• Graph comparison meets Alexandrov
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• An intrinsic characterization of five points in a $\mathrm{CAT}(0)$ space
• Finite flat spaces