Harmonic functions, entropy, and a characterization of the hyperbolic space

DOI10.1007/s12220-007-9001-zzbMath1151.53040arXiv0711.4592OpenAlexW2083641805MaRDI QIDQ941849

Xiaodong Wang

Publication date: 2 September 2008

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4592

zbMATH Keywords

entropyharmonic functions\(L^{2}\) spectrum

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Rigidity results (53C24) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (2)

Maximal bottom of spectrum or volume entropy rigidity in Alexandrov geometry ⋮ On the gradient estimate of Cheng and Yau

Cites Work

• Harmonic measures and Bowen-Margulis measures
• Random walks on discrete groups: Boundary and entropy
• On compact asymptotically harmonic manifolds
• Eigenvalue comparison theorems and its geometric applications
• On conformally compact Einstein manifolds.
• Complete manifolds with positive spectrum
• Complete manifolds with positive spectrum. II.
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• The spectrum of an asymptotically hyperbolic Einstein manifold
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds
• Riemannian Geometry
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