Locally nearly spherical surfaces are almost-positively c-curved

2010/09/18 by Philippe Delanoë, Delanoë, Philippe, Yuxin Ge +1 · 1 citation
Mathematics · #49N60 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1009.3586

openalex publication_date 2010/09/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The c-curvature of a complete surface with Gauss curvature close to 1 in C² 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.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions

Cited by

• A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds

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