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arXiv · 2608.02369

Poincar\'e inequalities on hyperbolic-type spaces

Anna Mc Court·Federico Santagati·Maria Vallarino
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Abstract

We establish global $L^p$-Poincar\'e inequalities, for $ p\in[1,\infty)$, on a class of nondoubling hyperbolic-type metric measure spaces. The proof relies on a discretisation of the space, which gives rise to a Gromov hyperbolic graph, called spiderweb, quasi-isometric to the original space. We prove global Poincar\'e inequalities for spiderwebs endowed with suitable measures and develop a general transference principle from discrete graphs to metric measure spaces. Combining these results yields global Poincar\'e inequalities under natural geometric and measure assumptions on the base space.

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BibTeXRIS

Anna Mc Court, Federico Santagati, Maria Vallarino. 2026-08-03. Poincar\'e inequalities on hyperbolic-type spaces. https://arxiv.org/abs/2608.02369

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