Accepted Paper
(2010)
Authors:
Alessio Figalli - Ludovic Rifford - Cédric Villani
Journal: Calc. Var. Partial Differential Equations [MathSciNet]
Abstract:
We investigate the properties of the Ma-Trudinger-Wang nonlocal
curvature tensor in the case of surfaces. In particular, we prove that a strict form
of the Ma-Trudinger-Wang condition is stable under C4 perturbation if the nonfocal domains
are uniformly convex; and we present new examples of positively curved surfaces which do not
satisfy the Ma-Trudinger-Wang condition. As a corollary of our results, optimal transport maps on a ``sufficiently flat'' ellipsoid are in general nonsmooth.![[PS]](/style/ps.png)
![[PDF]](/style/pdf.png)
[BibTeX Entry]
Available Files:
FRV-surface-CVPDE.pdf
abstract.tex (abstract.ps, abstract.pdf)
