Journal of Differential Geometry

Total positive curvature of hypersurfaces with convex boundary

Jaigyoung Choe, Mohammad Ghomi, and Manuel Ritoré


We prove that if Σ is a compact hypersurface in Euclidean space Rn, its boundary lies on the boundary of a convex body C, and meets C orthogonally from the outside, then the total positive curvature of Σ is bigger than or equal to half the area of the sphere Sn-1. Also, we obtain necessary and sufficient conditions for the equality to hold.

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J. Differential Geom., Volume 72, Number 1 (2006), 129-147.

First available in Project Euclid: 28 March 2006

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Choe, Jaigyoung; Ghomi, Mohammad; Ritoré, Manuel. Total positive curvature of hypersurfaces with convex boundary. J. Differential Geom. 72 (2006), no. 1, 129--147. doi:10.4310/jdg/1143593128.

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