Generalized Liouville theorem in nonnegatively curved Alexandrov spaces

DOI10.1007/s11401-008-0376-3zbMath1190.46059OpenAlexW1980085770MaRDI QIDQ1044797

Bobo Hua

Publication date: 15 December 2009

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-008-0376-3

zbMATH Keywords

Harnack inequalityharmonic functionAlexandrov space

Mathematics Subject Classification ID

Distributions and generalized functions on nonlinear spaces (46T30) Differential geometric aspects of harmonic maps (53C43) Special maps on metric spaces (54E40) Infinite-dimensional manifolds (46T05)

Related Items (8)

Curvature notions on graphs ⋮ Mean value property in limit for eigenfunctions of the Laplace–Beltrami operator ⋮ A Liouville-type theorem for smooth metric measure spaces ⋮ Polynomial growth harmonic functions on finitely generated Abelian groups ⋮ Parabolic Harnack inequality on metric spaces with a generalized volume property ⋮ Harmonic functions of polynomial growth on singular spaces with nonnegative Ricci curvature ⋮ Alexandrov spaces with large volume growth ⋮ Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II

Cites Work

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• Weyl type bounds for harmonic functions
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• A.D. Alexandrov spaces with curvature bounded below
• Harmonic functions on Alexandrov spaces and their applications
• Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces

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