Regularity of optimal transport andcut locus: From nonsmooth analysis to geometry to smooth analysis

Cédric Villani

doi:10.3934/dcds.2011.30.559

Article Contents

2011, Volume 30, Issue 2: 559-571. Doi: 10.3934/dcds.2011.30.559 open access

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Regularity of optimal transport and cut locus: From nonsmooth analysis to geometry to smooth analysis

Cédric Villani^1,

1.
Institut Henri Poincaré & Université Claude Bernard Lyon 1, 11 rue Pierre et Marie Curie 75230 Paris Cedex 05

Received: July 31, 2010

Published: May 2011

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Abstract

In this survey paper I describe the convoluted links between theregularity theory of optimal transport and the geometry of cut locus.

Keywords:

Optimal transport,
fully nonlinear partial differential equations,
Ma-Trudinger-Wang curvature,
cut locus.

Mathematics Subject Classification: 35J60, 53A05.

Citation:

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References

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