Bipolar comparison

Lebedeva, N; Petrunin, A; Zolotov, V

Lebedeva, N (reprint author), Steklov Inst, 27 Fontanka, St Petersburg 191023, Russia.; Lebedeva, N (reprint author), St Petersburg State Univ, Math Dept, Univ Sky Pr 28, Stary Peterhof 198504, Russia.

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2019; 29 (1): 258

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.

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