Normal cones, barrier cones, and the “spherical image” of convex surfaces in locally convex spaces

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Abstract

This paper discusses relations between a closed, convex set in a locally convex space and its normal cones and barrier cone in the dual space. Results of Wu and de Andrade on the Gauss map and spherical image of a convex hypersurface in a Hubert space are generalized to the topological vector space situation, and additional information is obtained on the relation of the interior of the spherical image and barrier cone to the size and shape of the given convex set.

Original languageEnglish (US)
Pages (from-to)107-123
Number of pages17
JournalPacific Journal of Mathematics
Volume70
Issue number2
StatePublished - 1977

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Convex Surface
Normal Cone
Locally Convex Space
Convex Sets
Cone
Gauss Map
Hubert Space
Topological Vector Space
Dual space
Hypersurface
Interior
Closed

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Normal cones, barrier cones, and the “spherical image” of convex surfaces in locally convex spaces",
abstract = "This paper discusses relations between a closed, convex set in a locally convex space and its normal cones and barrier cone in the dual space. Results of Wu and de Andrade on the Gauss map and spherical image of a convex hypersurface in a Hubert space are generalized to the topological vector space situation, and additional information is obtained on the relation of the interior of the spherical image and barrier cone to the size and shape of the given convex set.",
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