Pseudo-cones
Metric Geometry
2023-10-24 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2305.00452,
title = {Pseudo-cones},
author = {Rolf Schneider},
journal= {arXiv preprint arXiv:2305.00452},
year = {2023}
}
Comments
20 pages