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.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
localsemiconvkantpot.pdf
non disponibili
Licenza:
Non specificato
Dimensione
220.54 kB
Formato
Adobe PDF
|
220.54 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
