LOCALLY NEARLY SPHERICAL SURFACES ARE ALMOST-POSITIVELY c-CURVED

Abstract : 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.
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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⟩

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