The Liouville's theorem of harmonic functions on Alexandrov spaces with nonnegative Ricci curvature

DOI10.1007/s13226-015-0107-xzbMath1335.53093OpenAlexW2073647385WikidataQ125906068 ScholiaQ125906068MaRDI QIDQ5963331

Zhen-Hua Jiao, Qiang Li

Publication date: 7 March 2016

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-015-0107-x

zbMATH Keywords

harmonic functionRicci curvatureheat kernelAlexandrov spaceLiouville's theorem

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Heat kernel (35K08)

Cites Work

• Ricci curvature on Alexandrov spaces and rigidity theorems
• Existence and uniqueness of optimal maps on Alexandrov spaces
• Differentiability of Lipschitz functions on metric measure spaces
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• Yau's gradient estimates on Alexandrov spaces
• Ricci curvature for metric-measure spaces via optimal transport
• On the geometry of metric measure spaces. I
• Semiconcave functions in Alexandrov's geometry
• Harmonic functions on complete riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
• A.D. Alexandrov spaces with curvature bounded below
• Harmonic functions on Alexandrov spaces and their applications
• Infinitesimal Bishop-Gromov condition for Alexandrov spaces
• Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces

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