New results on noncompact harmonic manifolds

DOI10.4171/CMH/265zbMath1287.53056arXiv0910.3872MaRDI QIDQ439893

Gerhard Knieper

Publication date: 17 August 2012

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.3872

zbMATH Keywords

conjugate pointsgeodesic flowhorosphereexponential volume growthharmonic manifoldLichnerowicz conjecture

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Foliations (differential geometric aspects) (53C12)

Related Items (15)

Harmonic functions on rank one asymptotically harmonic manifolds ⋮ The Fourier transform on harmonic manifolds of purely exponential volume growth ⋮ Harmonic manifolds of hypergeometric type and spherical Fourier transform ⋮ The shifted wave equation on non-flat harmonic manifolds ⋮ Dynamics of \(L^p\) multipliers on harmonic manifolds ⋮ Boundaries of non-compact harmonic manifolds ⋮ Harmonic manifolds and tubes ⋮ Integral geometric properties of non-compact harmonic spaces ⋮ Entropy rigidity of symmetric spaces without focal points ⋮ Submanifolds, isoperimetric inequalities and optimal transportation ⋮ Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces ⋮ The marked length spectrum of Anosov manifolds ⋮ Harmonic Hadamard manifolds and Gauss hypergeometric differential equations ⋮ Information geometry of Busemann-barycenter for probability measures ⋮ Geodesic stretch, pressure metric and marked length spectrum rigidity

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