Rough isometry and the asymptotic Dirichlet problem

DOI10.2748/tmj/1178224933zbMath0928.58030OpenAlexW2037463148MaRDI QIDQ1281709

Yong Hah Lee, Hyeong In Choi, Seok Woo Kim

Publication date: 4 January 2000

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178224933

zbMATH Keywords

Dirichlet problemharmonic functionSobolev inequalityboundary at infinityrough isometryasymptotic boundary

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Boundary value problems on manifolds (58J32) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Discrete potential theory (31C20)

Related Items (2)

Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces ⋮ Asymptotic Dirichlet problem for the Schrödinger operator via rough isometry

Cites Work

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• Rough isometries, and combinatorial approximations of geometries of non- compact Riemannian manifolds
• The Dirichlet problem at infinity for manifolds of negative curvature
• The Dirichlet problem at infinity for a negatively curved manifold
• Rough isometries and the parabolicity of Riemannian manifolds
• Positive harmonic functions on complete manifolds of negative curvature
• The chromatic index of a graph whose core has maximum degree two
• Isometric Riemannian manifolds at infinity
• Visibility manifolds
• Asymptotic Dirichlet Problems for Harmonic Functions on Riemannian Manifolds
• A note on the isoperimetric constant

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