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arXiv · 2106.01701

Geometric Hardy inequalities via integration on flows

Miltiadis Paschalis
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Abstract

We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities and the explicit optimal Hardy potentials that are induced by this method. We then apply the method to retrieve some known inequalities and establish some new ones.

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Miltiadis Paschalis. 2021-06-03. Geometric Hardy inequalities via integration on flows. https://arxiv.org/abs/2106.01701

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