Harmonic manifolds with mimimal horospheres

DOI10.1007/BF02930658zbMath1066.53086MaRDI QIDQ1407747

Hemangi Shah, Akhil Ranjan

Publication date: 21 October 2003

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

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (12)

Unnamed Item ⋮ The Fourier transform on harmonic manifolds of purely exponential volume growth ⋮ Harmonic manifolds of hypergeometric type and spherical Fourier transform ⋮ Characterizing the harmonic manifolds by the eigenfunctions of the Laplacian ⋮ MEAN-VALUE PROPERTY ON MANIFOLDS WITH MINIMAL HOROSPHERES ⋮ Boundaries of non-compact harmonic manifolds ⋮ Harmonic functions on metric measure spaces ⋮ A new proof of the theorem: Harmonic manifolds with minimal horospheres are flat ⋮ Submanifolds, isoperimetric inequalities and optimal transportation ⋮ Differential geometry in India ⋮ Harmonic spaces and density functions ⋮ Harmonic Hadamard manifolds and Gauss hypergeometric differential equations

Cites Work

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• Jacobi tensors and Ricci curvature
• Horospheres and the stable part of the geodesic flow
• The Lichnerowicz conjecture on harmonic manifolds
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• Busemann functions in a harmonic manifold
• The volume of a small geodesic ball of a Riemannian manifold
• Riemannian manifold, global mean value inequality, Laplace equation, heat equation, weak volume growth condition
• Mean Value Theorems in Harmonic Riemannian Spaces
• Sur les espaces riemanniens complètement harmoniques

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