We prove that any Kantorovich potential for the distance-squared cost function on a Riemannian manifold is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full \mu-measure as soon as the starting measure \mu does not charge n – 1-dimensional rectifiable sets.

Local semiconvexity of Kantorovich potentials on non-compact manifolds / Gigli, Nicola; Figalli, Alessio. - In: ESAIM. COCV. - ISSN 1292-8119. - 17:3(2011), pp. 648-653. [10.1051/cocv/2010011]

Local semiconvexity of Kantorovich potentials on non-compact manifolds

Gigli, Nicola;
2011-01-01

Abstract

We prove that any Kantorovich potential for the distance-squared cost function on a Riemannian manifold is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full \mu-measure as soon as the starting measure \mu does not charge n – 1-dimensional rectifiable sets.
2011
17
3
648
653
Gigli, Nicola; Figalli, Alessio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14212
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