Liouville properties for 𝑝-harmonic maps with finite 𝑞-energy

DOI10.1090/tran/6351zbMath1339.53034arXiv1211.2899OpenAlexW2964320087MaRDI QIDQ2796507

Shihshu Walter Wei, Shu-Cheng Chang, Jui-Tang Chen

Publication date: 29 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2899

zbMATH Keywords

\(p\)-harmonic mapLiouville-type properties\(p\)-hyperbolic endperturbed \(p\)-Laplace operatorweakly \(p\)-harmonic function

Mathematics Subject Classification ID

Harmonic maps, etc. (58E20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (19)

Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds ⋮ Comparison Theorems in Riemannian Geometry with Applications ⋮ \(p\)-harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold ⋮ \(L^2\) curvature pinching theorems and vanishing theorems on complete Riemannian manifolds ⋮ Vanishing theorems for \(p\)-harmonic forms on Riemannian manifolds ⋮ Rigidity properties of smooth metric measure spaces via the weighted 𝑝-Laplacian ⋮ Geometric aspects of \(p\)-capacitary potentials ⋮ Liouville type theorems for nonlinear \(p\)-Laplacian equation on complete noncompact Riemannian manifolds ⋮ Boundary regularity of stationary critical points for a Cosserat energy functional ⋮ Vanishing theorem for \(p\)-harmonic 1-forms on complete submanifolds in spheres ⋮ Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space ⋮ Liouville theorems for nonlinear elliptic equations on Riemannian manifolds ⋮ Complete Pseudohermitian manifolds with positive spectrum ⋮ Exponentially harmonic maps of complete Riemannian manifolds ⋮ \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality ⋮ Dualities in comparison theorems and bundle-valued generalized harmonic forms on noncompact manifolds ⋮ Gradient estimate and Liouville theorems for \(p\)-harmonic maps ⋮ The \(p\)-eigenvalue estimates and \(L^q\)\( p\)-harmonic forms on submanifolds of Hadamard manifolds ⋮ Regularity Issues for Cosserat Continua and $p$-Harmonic Maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global comparison principles for the \(p\)-Laplace operator on Riemannian manifolds
• On vanishing theorems for vector bundle valued \(p\)-forms and their applications
• Everywhere-regularity for some quasilinear systems with a lack of ellipticity
• Motion of level sets by mean curvature. I
• Generalizations of the uniformization theorem and Bochner's method in \(p\)-harmonic geometry
• Asymptotic Dirichlet problem on negatively curved spaces
• Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set
• The existence of minimal immersions of 2-spheres
• Complete surfaces with finite total curvature
• Harmonic functions and the structure of complete manifolds
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• Regularity for a class of nonlinear elliptic systems
• Capacitary functions in convex rings
• Solutions of elliptic equations on manifolds with roughly Euclidean ends
• The inverse mean curvature flow and the Riemannian Penrose inequality
• On \(p\)-harmonic morphisms
• Parabolicity of manifolds
• Complete manifolds with positive spectrum
• Complete manifolds with positive spectrum. II.
• A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
• A classification and some constructions of \(p\)-harmonic morphisms
• Green's functions, harmonic functions, and volume comparison
• A sharp \(L^q\)-Liouville theorem for \(p\)-harmonic functions
• Volume growth, Green's functions, and parabolicity of ends
• 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
• On some non-linear elliptic differential functional equations
• Linear and quasilinear elliptic equations
• Volume growth and parabolicity
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Weighted Poincaré inequality and rigidity of complete manifolds
• Local gradient estimates of $p$-harmonic functions, $1/H$-flow, and an entropy formula
• Mappings minimizing theLp norm of the gradient
• Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds
• On some regular multiple integral problems in the calculus of variations
• Harnack inequality and hyperbolicity for subelliptic \(p\)-Laplacians with applications to Picard type theorems

This page was built for publication: Liouville properties for 𝑝-harmonic maps with finite 𝑞-energy