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Journal of Convex Analysis 16 (2009), No. 3, 939--957
Copyright Heldermann Verlag 2009

External Analysis of Boundary Points of Convex Sets: Supporting Cones and Drops

José Pedro Moreno
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma, Madrid 28049, Spain

Alberto Seeger
Department of Mathematics, University of Avignon, 33 rue Louis Pasteur, 84000 Avignon, France

Let K be a solid closed convex set in a normed space. We study the geometry of the boundary of K with the help of some multivalued maps defined on the exterior of K. Supporting cones and drops are the main tools of analysis.

Keywords: Convex set, boundary point, supporting cone, drop, multivalued map.

MSC: 49J53, 52A07

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