Radial measures of pseudo-cones
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911366202261504 |
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| author | Schneider, Rolf |
| author_facet | Schneider, Rolf |
| contents | We consider $C$-pseudo-cones, that is, closed convex sets $K \subset{\mathbb R}^n$ with $o\notin K\subset C$, for which $C$ is the recession cone. Here $C$ is a given closed convex cone in ${\mathbb R}^n$, pointed and with nonempty interior. We define a class of measures for such pseudo-cones and show how they can be interpreted as derivative measures. For a subclass of these measures, namely for dual curvature measures with negative indices, we solve a Minkowski type existence problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Radial measures of pseudo-cones Schneider, Rolf Metric Geometry 52A20 We consider $C$-pseudo-cones, that is, closed convex sets $K \subset{\mathbb R}^n$ with $o\notin K\subset C$, for which $C$ is the recession cone. Here $C$ is a given closed convex cone in ${\mathbb R}^n$, pointed and with nonempty interior. We define a class of measures for such pseudo-cones and show how they can be interpreted as derivative measures. For a subclass of these measures, namely for dual curvature measures with negative indices, we solve a Minkowski type existence problem. |
| title | Radial measures of pseudo-cones |
| topic | Metric Geometry 52A20 |
| url | https://arxiv.org/abs/2601.06594 |