# LOCALLY NEARLY SPHERICAL SURFACES ARE ALMOST-POSITIVELY c-CURVED

1 Géométrie, Analyse et Dynamique
JAD - Laboratoire Jean Alexandre Dieudonné
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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Journal articles

Cited literature [16 references]

https://hal.univ-cotedazur.fr/hal-00864833
Contributor : Philippe Delanoë <>
Submitted on : Monday, September 23, 2013 - 1:10:24 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:03 PM
Long-term archiving on : Tuesday, December 24, 2013 - 4:31:19 AM

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MAA_18_3_02-del.pdf
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• HAL Id : hal-00864833, version 1

### Citation

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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