Methods and Applications of Analysis
Volume 18 (2011)
Locally nearly spherical surfaces are almost-positively $c$-curved
Pages: 269 – 302
The $c$-curvature of a complete surface with Gauss curvature close to 1 in $C2$ norm is almost-positive (in the sense of Kim–McCann). Our proof goes by a careful case by case analysis combined with perturbation arguments from the constant curvature case, keeping track of an estimate on the closeness curvature condition.
Monge problem, quadratic cost, compact surfaces, nearly spherical, positive ccurvature, stability
2010 Mathematics Subject Classification
Primary 53C21. Secondary 49N60.