On the homotopy class of maps with finite \(p\)-energy into non-positively curved manifolds

DOI10.1007/s10711-009-9376-zzbMath1186.53076OpenAlexW2083201220MaRDI QIDQ845789

Stefano Pigola, Giona Veronelli

Publication date: 29 January 2010

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-009-9376-z

zbMATH Keywords

Liouville type theoremhomotopy class\(p\)-harmonic map

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20)

Related Items

A general comparison theorem for \(p\)-harmonic maps in homotopy class ⋮ The connectivity at infinity of a manifold and \(L^{q, p}\)-Sobolev inequalities ⋮ Path and quasi-homotopy for Sobolev maps between manifolds ⋮ Liouville type theorem about \(p\)-harmonic function and \(p\)-harmonic map with finite \(L^q\)-energy ⋮ Existence of \(p\)-energy minimizers in homotopy classes and lifts of Newtonian maps ⋮ Global comparison principles for the \(p\)-Laplace operator on Riemannian manifolds ⋮ Exponentially harmonic maps of complete Riemannian manifolds ⋮ On the Dirichlet problem for \(p\)-harmonic maps. I: Compact targets ⋮ Gradient estimate and Liouville theorems for \(p\)-harmonic maps ⋮ REMARKS ON L^p-VANISHING RESULTS IN GEOMETRIC ANALYSIS

Cites Work

• On removable singularities of p-harmonic maps
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• A Liouville type theorem for \(p\)-harmonic maps
• Vanishing and finiteness results in geometric analysis. A generalization of the Bochner technique
• Constancy of \(p\)-harmonic maps of finite \(q\)-energy into non-positively curved manifolds
• Vanishing theorems on Riemannian manifolds, and geometric applications
• Harmonic Maps of Finite Energy From Non-Compact Manifolds
• A maximum principle for 𝑃-harmonic maps with 𝐿^{𝑞} finite energy