Optimal Poincaré-Hardy-type Inequalities on Manifolds and Graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915162479394816 |
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| author | Fischer, Florian Rose, Christian |
| author_facet | Fischer, Florian Rose, Christian |
| contents | We review a method to obtain optimal Poincaré-Hardy-type inequalities on the hyperbolic spaces, and discuss briefly generalisations to certain classes of Riemannian manifolds.
Afterwards, we recall a corresponding result on homogeneous regular trees and provide a new proof using the aforementioned method. The same strategy will then be applied to obtain new optimal Hardy-type inequalities on weakly spherically symmetric graphs which include fast enough growing trees and anti-trees. In particular, this yields optimal weights which are larger at infinity than the optimal weights classically constructed via the Fitzsimmons ratio of the square root of the minimal positive Green's function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Poincaré-Hardy-type Inequalities on Manifolds and Graphs Fischer, Florian Rose, Christian Analysis of PDEs Spectral Theory 35B09, 26D10, 31C12, 31C20, 35B09, 39A12, 58J60 We review a method to obtain optimal Poincaré-Hardy-type inequalities on the hyperbolic spaces, and discuss briefly generalisations to certain classes of Riemannian manifolds. Afterwards, we recall a corresponding result on homogeneous regular trees and provide a new proof using the aforementioned method. The same strategy will then be applied to obtain new optimal Hardy-type inequalities on weakly spherically symmetric graphs which include fast enough growing trees and anti-trees. In particular, this yields optimal weights which are larger at infinity than the optimal weights classically constructed via the Fitzsimmons ratio of the square root of the minimal positive Green's function. |
| title | Optimal Poincaré-Hardy-type Inequalities on Manifolds and Graphs |
| topic | Analysis of PDEs Spectral Theory 35B09, 26D10, 31C12, 31C20, 35B09, 39A12, 58J60 |
| url | https://arxiv.org/abs/2501.18379 |