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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| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2025
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| Summary: | 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. |
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