Length averages for codimension one foliations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913571229663232 |
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| author | Asaoka, Masayuki Nakano, Yushi Varandas, Paulo Yokoyama, Tomoo |
| author_facet | Asaoka, Masayuki Nakano, Yushi Varandas, Paulo Yokoyama, Tomoo |
| contents | In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group structure itself, to obtain irregular behavior of ball averages for certain non-amenable group actions. Several geometric realization results show that any such groups can appear connected with the topology of leaves which are connected sums of plugs with a special geometry, namely nearly equidistant boundary components. This is used to produce the first examples of codimension one $\mathcal C^\infty$ regular foliations on a compact Riemannian manifold $M$ for which the length average of some continuous function does not exist on a non-empty open subset of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Length averages for codimension one foliations Asaoka, Masayuki Nakano, Yushi Varandas, Paulo Yokoyama, Tomoo Dynamical Systems Geometric Topology In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group structure itself, to obtain irregular behavior of ball averages for certain non-amenable group actions. Several geometric realization results show that any such groups can appear connected with the topology of leaves which are connected sums of plugs with a special geometry, namely nearly equidistant boundary components. This is used to produce the first examples of codimension one $\mathcal C^\infty$ regular foliations on a compact Riemannian manifold $M$ for which the length average of some continuous function does not exist on a non-empty open subset of $M$. |
| title | Length averages for codimension one foliations |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2411.02106 |