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arXiv · 2503.04703

Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds

Cristian Ciulică·Teodor Rugină
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Abstract

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.

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Cristian Ciulică, Teodor Rugină. 2025-03-06. Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds. https://arxiv.org/abs/2503.04703

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