Locally nearly spherical surfaces are almost-positively $c$-curved

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

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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