Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917947201552384 |
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| author | Ciulică, Cristian Rugină, Teodor |
| author_facet | Ciulică, Cristian Rugină, Teodor |
| contents | In this paper we prove sharp multipolar Hardy-type inequalities in the Riemannian $L^p-$setting for $p\geq 2$ using the method of super-solutions and fundamental results from comparison theory on manifolds, thus generalizing previous results for $p=2$. We emphasize that when we restrict to Cartan-Hadamard manifolds, the inequalities improve in the case $2<p<N$ compared to the case $p=2$ since we obtain positive remainder terms which are controlled by curvature estimates. In the end, we treat the cases of positive and negative constant sectional curvature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_04703 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds Ciulică, Cristian Rugină, Teodor Analysis of PDEs 35A23, 35B25, 53C21, 58J60 In this paper we prove sharp multipolar Hardy-type inequalities in the Riemannian $L^p-$setting for $p\geq 2$ using the method of super-solutions and fundamental results from comparison theory on manifolds, thus generalizing previous results for $p=2$. We emphasize that when we restrict to Cartan-Hadamard manifolds, the inequalities improve in the case $2<p<N$ compared to the case $p=2$ since we obtain positive remainder terms which are controlled by curvature estimates. In the end, we treat the cases of positive and negative constant sectional curvature. |
| title | Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds |
| topic | Analysis of PDEs 35A23, 35B25, 53C21, 58J60 |
| url | https://arxiv.org/abs/2503.04703 |