Bipolar comparison

26 Nov 2017 · Nina Lebedeva, Anton Petrunin, Vladimir Zolotov ·

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.