Total positive curvature of hypersurfaces with convex boundary
Choe, Jaigyoung ; Ghomi, Mohammad ; Ritoré, Manuel
J. Differential Geom., Tome 72 (2006) no. 1, p. 129-147 / Harvested from Project Euclid
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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.
Publié le : 2006-01-14
Classification:  
@article{1143593128,
     author = {Choe, Jaigyoung and Ghomi, Mohammad and Ritor\'e, Manuel},
     title = {Total positive curvature of hypersurfaces with convex boundary},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 129-147},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1143593128}
}

Choe, Jaigyoung; Ghomi, Mohammad; Ritoré, Manuel. Total positive curvature of hypersurfaces with convex boundary. J. Differential Geom., Tome 72 (2006) no. 1, pp.  129-147. http://gdmltest.u-ga.fr/item/1143593128/