The singular Weinstein conjecture
In this article, we investigate Reeb dynamics on bm-contact manifolds, previously introduced in [37], which are contact away from a hypersurface Zbut satisfy certain transversality conditions on Z. The study of these contact structures is motivated by that of contact manifolds with boundary. The sea...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/350252 |
| Acceso en línea: | https://hdl.handle.net/2117/350252 https://dx.doi.org/10.1016/j.aim.2021.107925 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematical analysis Geometry Reeb dynamics Contact geometry Anàlisi matemàtica Geometria Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | In this article, we investigate Reeb dynamics on bm-contact manifolds, previously introduced in [37], which are contact away from a hypersurface Zbut satisfy certain transversality conditions on Z. The study of these contact structures is motivated by that of contact manifolds with boundary. The search of periodic Reeb orbits on those manifolds thereby starts with a generalization of the well-known Weinstein conjecture. Contrary to the initial expectations, examples of compact bm-contact manifolds without periodic Reeb orbits outside Zare provided. Furthermore, we prove that in dimension 3, there are always infinitely many periodic orbits on the critical set if it is compact. We prove that traps for the bm-Reeb flow exist in any dimension. This investigation goes hand-in-hand with the Weinstein conjecture on non-compact manifolds having compact ends of convex |
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