The convex hull property and topology of hypersurfaces with nonnegative curvature.

DOI10.1016/S0001-8708(03)00006-9zbMath1050.53008MaRDI QIDQ1418006

Stephanie B. Alexander, Mohammad Ghomi

Publication date: 6 January 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

convex hullnonnegative curvatureconvergence theoremclippingconvex caplocally convex surface

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (7)

Positively curved surfaces with no tangent support plane ⋮ Nonnegatively curved hypersurfaces with free boundary on a sphere ⋮ Convexity, rigidity, and reduction of codimension of isometric immersions into space forms ⋮ Maximum principles for vectorial approximate minimizers of nonconvex functionals ⋮ Topology of Riemannian submanifolds with prescribed boundary ⋮ 𝐡-principles for hypersurfaces with prescribed principle curvatures and directions ⋮ Isoperimetric inequalities in Euclidean convex bodies

Cites Work

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• Nonnegatively curved ends of Euclidean hypersurfaces
• Limite d'hypersurfaces localement convexes. (Limit of locally convex hypersurfaces)
• Une relation entre diamètre extrinsèque, intégrale de la courbure de Gauss et inradius pour les hypersurfaces localement convexes d'un espace euclidien. (A relation between external diameter, Gaussian curvature integral and inradius for locally convex hypersurfaces of a Euclidean space)
• Sufficient criteria of convexity
• Embedding and knotting of positive curvature surfaces in 3-space
• Strictly convex submanifolds and hypersurfaces of positive curvature.
• The existence of hypersurfaces of constant Gauss curvature with prescribed boundary.
• The convex hull property of immersed manifolds
• On the rigidity of punctured ovaloids. II
• Convex sets in linear spaces
• On Spherical Image Maps Whose Jacobians Do Not Change Sign
• Partial Differential Relations
• Knots are Determined by Their Complements
• Total Curvature of Manifolds with Boundary in Eⁿ
• The convex hull property of noncompact hypersurfaces with positive curvature
• Elementary Differential Topology. (AM-54)
• On Hypersurfaces with no Negative Sectional Curvatures
• Locally Convex Hypersurfaces
• On locally convex manifolds
• Gauss map, topology, and convexity of hypersurfaces with nonvanishing curvature

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