Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds

Details Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds

2007-09-11

arxiv.org/abs/0709.1653v1

Mathematics

Differential Geometry

10 pages

Scientific paper

Counterexamples to continuity of optimal transportation on Riemannian
manifolds with everywhere positive sectional curvature are provided. These
examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed
by positivity of sectional curvature.

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