Faces of invariant convex sets in representations of nontrivial copolarity
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914468937596928 |
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| author | Shi, Yi |
| author_facet | Shi, Yi |
| contents | Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $Σ$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P=E\capΣ$ is a convex set in $Σ$. We prove that up to conjugacy the face structure of $E$ is completely determined by that of $P$ and that a face of $E$ is exposed if and only if the corresponding face of $P$ is exposed. Our result generalizes the result proved by Leonardo Biliotti, Alessandro Ghigi and Peter Heinzner in the case where $(V, G)$ is a polar representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11147 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Faces of invariant convex sets in representations of nontrivial copolarity Shi, Yi Differential Geometry Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $Σ$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P=E\capΣ$ is a convex set in $Σ$. We prove that up to conjugacy the face structure of $E$ is completely determined by that of $P$ and that a face of $E$ is exposed if and only if the corresponding face of $P$ is exposed. Our result generalizes the result proved by Leonardo Biliotti, Alessandro Ghigi and Peter Heinzner in the case where $(V, G)$ is a polar representation. |
| title | Faces of invariant convex sets in representations of nontrivial copolarity |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.11147 |