Pseudo-cones

Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the interior. The purpose of the following is to study this analogy in g...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 155; p. 102657
Main Author Schneider, Rolf
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2024
Subjects
C-close set
Conjugate face
Copolarity
Minkowski's existence theorem
Pseudo-cone
Surface area measure
secondary
Minkowski's existence theorem
Surface area measure
Pseudo-cone
Conjugate face
C-close set
primary
Copolarity
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ISSN0196-8858
1090-2074
DOI10.1016/j.aam.2023.102657

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Summary:Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the interior. The purpose of the following is to study this analogy in greater detail. We supplement the investigation of copolarity, considering, for example, conjugate faces. Then we deal with the question suggested by Minkowski's theorem, asking which measures are surface area measures of pseudo-cones with given recession cone. We provide a sufficient condition for possibly infinite measures and a special class of pseudo-cones.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2023.102657