Vector-valued horofunction boundaries and Patterson--Sullivan measures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918417978621952 |
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| author | Kim, Dongryul M. Zimmer, Andrew |
| author_facet | Kim, Dongryul M. Zimmer, Andrew |
| contents | In higher rank, there is a well-studied theory of Patterson--Sullivan measures supported on partial flag manifolds. However, establishing the existence and uniqueness of such measures is a difficult question. In this paper, we develop a theory for Patterson--Sullivan measures supported on certain vector-valued horofunction boundaries of the associated symmetric space, where existence is straightforward. We also introduce a notion of shadows for this compactification and establish a shadow lemma. For transverse groups, we prove uniqueness and ergodicity results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28693 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vector-valued horofunction boundaries and Patterson--Sullivan measures Kim, Dongryul M. Zimmer, Andrew Geometric Topology Dynamical Systems Group Theory In higher rank, there is a well-studied theory of Patterson--Sullivan measures supported on partial flag manifolds. However, establishing the existence and uniqueness of such measures is a difficult question. In this paper, we develop a theory for Patterson--Sullivan measures supported on certain vector-valued horofunction boundaries of the associated symmetric space, where existence is straightforward. We also introduce a notion of shadows for this compactification and establish a shadow lemma. For transverse groups, we prove uniqueness and ergodicity results. |
| title | Vector-valued horofunction boundaries and Patterson--Sullivan measures |
| topic | Geometric Topology Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2603.28693 |