The convex hull property of noncompact hypersurfaces with positive curvature | Zendy

Stephanie Alexander | Zendy; Mohammad Ghomi | Zendy

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The convex hull property of noncompact hypersurfaces with positive curvature

Author(s) -

Stephanie Alexander,

Mohammad Ghomi

Publication year - 2004

Publication title -

american journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.818

H-Index - 67

eISSN - 1080-6377

pISSN - 0002-9327

DOI - 10.1353/ajm.2004.0023

Subject(s) - mathematics , convex hull , hypersurface , convex body , boundary (topology) , regular polygon , pure mathematics , curvature , property (philosophy) , hull , mathematical analysis , euclidean geometry , euclidean space , geometry , combinatorics , composite material , philosophy , epistemology , materials science

We prove that in Euclidean space Rⁿ⁺¹, every metrically complete, positively curved immersed hypersurface M, with compact boundary ∂M, lies outside the convex hull of ∂M provided that ∂M is embedded on the boundary of a convex body and n > 2. For n = 2, on the other hand, we construct examples which contradict this property.