Stability of p ‐parabolicity under quasi‐isometries

Ana Granados,Domingo Pestana,Ana Portilla,José M. Rodríguez

Mathematische Nachrichten（2022）

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摘要

Kanai proved the stability under quasi‐isometries of numerous global properties (including existence of Green's function, i.e., non‐parabolicity) between Riemannian manifolds of bounded geometry. Unfortunately, Kanai's hypotheses are not usually satisfied in the context of Riemann surfaces endowed with the Poincaré metric. In this work we prove the stability of p‐parabolicity (with 1

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关键词

Green's function, Liouville property, negative pinched curvature, Poincare metric, quasi-isometry, Riemann surface

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