Poincaré inequality for one forms on four manifolds with bounded Ricci curvature
In this short note, we provide a quantitative global Poincar´e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci curvature. This seems to be the first non-trivial result givi...
| Main Authors: | , |
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| 格式: | Journal article |
| 语言: | English |
| 出版: |
Springer
2025
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| _version_ | 1826317354739433472 |
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| author | Honda, S Mondino, A |
| author_facet | Honda, S Mondino, A |
| author_sort | Honda, S |
| collection | OXFORD |
| description | In this short note, we provide a quantitative global Poincar´e inequality for one forms on a closed Riemannian four manifold, in terms of an
upper bound on the diameter, a positive lower bound on the volume,
and a two-sided bound on Ricci curvature. This seems to be the first
non-trivial result giving such an inequality without any higher curvature
assumptions. The proof is based on a Hodge theoretic result on orbifolds,
a comparison for fundamental groups, and a spectral convergence with
respect to Gromov-Hausdorff convergence, via a degeneration result to
orbifolds by Anderson. |
| first_indexed | 2025-02-19T04:37:09Z |
| format | Journal article |
| id | oxford-uuid:ecf53023-3d6b-49b6-b83c-5a80d61a9f28 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:37:09Z |
| publishDate | 2025 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:ecf53023-3d6b-49b6-b83c-5a80d61a9f282025-02-03T09:20:37ZPoincaré inequality for one forms on four manifolds with bounded Ricci curvatureJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ecf53023-3d6b-49b6-b83c-5a80d61a9f28EnglishSymplectic ElementsSpringer2025Honda, SMondino, AIn this short note, we provide a quantitative global Poincar´e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci curvature. This seems to be the first non-trivial result giving such an inequality without any higher curvature assumptions. The proof is based on a Hodge theoretic result on orbifolds, a comparison for fundamental groups, and a spectral convergence with respect to Gromov-Hausdorff convergence, via a degeneration result to orbifolds by Anderson. |
| spellingShingle | Honda, S Mondino, A Poincaré inequality for one forms on four manifolds with bounded Ricci curvature |
| title | Poincaré inequality for one forms on four manifolds with bounded Ricci curvature |
| title_full | Poincaré inequality for one forms on four manifolds with bounded Ricci curvature |
| title_fullStr | Poincaré inequality for one forms on four manifolds with bounded Ricci curvature |
| title_full_unstemmed | Poincaré inequality for one forms on four manifolds with bounded Ricci curvature |
| title_short | Poincaré inequality for one forms on four manifolds with bounded Ricci curvature |
| title_sort | poincare inequality for one forms on four manifolds with bounded ricci curvature |
| work_keys_str_mv | AT hondas poincareinequalityforoneformsonfourmanifoldswithboundedriccicurvature AT mondinoa poincareinequalityforoneformsonfourmanifoldswithboundedriccicurvature |