LOCALLY NEARLY SPHERICAL SURFACES ARE ALMOST-POSITIVELY c-CURVED

Philippe Delanoë (1) , Yuxin Ge (2)

1 Géométrie, Analyse et Dynamique
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The $c$-curvature of a complete surface with Gauss curvature close to 1 in $C^2$ 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.

Mots clés: Monge problem; quadratic cost; compact surfaces; nearly spherical; positive $c$-curvature; stability

Domaines: Géométrie différentielle [math.DG]

Philippe Delanoë, Yuxin Ge. LOCALLY NEARLY SPHERICAL SURFACES ARE ALMOST-POSITIVELY c-CURVED. Methods and Applications of Analysis, 2012, 18 (3), pp.269-302. ⟨hal-00864833⟩