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

Philippe Delanoë; Yuxin Ge

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arXiv · 1009.3586

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

Philippe Delanoë·Yuxin Ge

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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. 2012-03-22. Locally nearly spherical surfaces are almost-positively $c$-curved. https://arxiv.org/abs/1009.3586

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