Let be a geodesic metric measure space. Consider a geodesic in the -Wasserstein space. Then as goes to, the support of and the support of have to overlap, provided an upper bound on the densities holds. We give a more precise formulation of this self-intersection property. Given a geodesic of and, we consider the set of times for which this geodesic belongs to the support of. We prove that is a point of Lebesgue density 1 for this set, in the integral sense. Our result applies to spaces satisfying. The non-branching property is not needed.
Self-intersection of optimal geodesics / F. Cavalletti, M. Huesmann. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 46:3(2014 Jun), pp. 653-656. [10.1112/blms/bdu026]
Self-intersection of optimal geodesics
F. Cavalletti
Primo
;
2014
Abstract
Let be a geodesic metric measure space. Consider a geodesic in the -Wasserstein space. Then as goes to, the support of and the support of have to overlap, provided an upper bound on the densities holds. We give a more precise formulation of this self-intersection property. Given a geodesic of and, we consider the set of times for which this geodesic belongs to the support of. We prove that is a point of Lebesgue density 1 for this set, in the integral sense. Our result applies to spaces satisfying. The non-branching property is not needed.
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Bulletin of London Math Soc - 2014 - Cavalletti - Self‐intersection of optimal geodesics.pdf
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