Volume growth and parabolicity

DOI10.1090/S0002-9939-01-05954-8zbMath0998.58024OpenAlexW1931459448WikidataQ110031542 ScholiaQ110031542MaRDI QIDQ2731941

Pekka Koskela, Ilkka Holopainen

Publication date: 30 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-05954-8

zbMATH Keywords

Green's functionharmonic functionvolume growthparabolicity

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (13)

Yamabe type equations with a sign-changing nonlinearity, and the prescribed curvature problem ⋮ Sharp capacity estimates for annuli in weighted \(\mathbf {R}^n\) and in metric spaces ⋮ Prime ends for domains in metric spaces ⋮ Classification of metric measure spaces and their ends using p-harmonic functions ⋮ Moduli spaces of critical Riemannian metrics with \(L^{\frac{n}{2}}\) norm curvature bounds ⋮ Existence and uniqueness of limits at infinity for homogeneous Sobolev functions ⋮ Volume growth, capacity estimates, \(p\)-parabolicity and sharp integrability properties of \(p\)-harmonic Green functions ⋮ The Liouville theorem for \(p\)-harmonic functions and quasiminimizers with finite energy ⋮ Global comparison principles for the \(p\)-Laplace operator on Riemannian manifolds ⋮ Liouville properties for 𝑝-harmonic maps with finite 𝑞-energy ⋮ Trace operators on regular trees ⋮ Topology of Kähler manifolds with weakly pseudoconvex boundary ⋮ Classification criteria for regular trees

Cites Work

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• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• A note on the existence of positive Green's function
• Quasiconformal maps in metric spaces with controlled geometry
• Green's functions, harmonic functions, and volume comparison
• Volume growth, Green's functions, and parabolicity of ends
• Positive Solutions of Quasilinear Elliptic Equations on Riemannian Manifolds
• A note on the isoperimetric constant
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

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