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Stability of p‐parabolicity under quasi‐isometries

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Listed:
  • Ana Granados
  • Domingo Pestana
  • Ana Portilla
  • José M. Rodríguez

Abstract

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

Suggested Citation

  • Ana Granados & Domingo Pestana & Ana Portilla & José M. Rodríguez, 2022. "Stability of p‐parabolicity under quasi‐isometries," Mathematische Nachrichten, Wiley Blackwell, vol. 295(3), pages 536-559, March.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:3:p:536-559
    DOI: 10.1002/mana.201900497
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