28 research outputs found
Liouville theorem for -harmonic maps under non-negative -Ricci curvature for non-positive
Let be a -vector field on an -dimensional complete Riemannian
manifold . We prove a Liouville theorem for -harmonic maps
satisfying various growth conditions from complete Riemannian manifolds with
non-negative -Ricci curvature for
into Cartan-Hadam\-ard
manifolds, which extends Cheng's Liouville theorem proved S.~Y.~Cheng for
sublinear growth harmonic maps from complete Riemannian manifolds with
non-negative Ricci curvature into Cartan-Hadamard manifolds. We also prove a
Liouville theorem for -harmonic maps from complete Riemannian manifolds with
non-negative -Ricci curvature for
into regular geodesic balls
of Riemannian manifolds with positive upper sectional curvature bound, which
extends the results of Hildebrandt-Jost-Wideman and Choi. Our probabilistic
proof of Liouville theorem for several growth -harmonic maps into Hadamard
manifolds enhances an incomplete argument by Stafford. Our results extend the
results due to Chen-Jost-Qiu\cite{ChenJostQiu} and Qiu\cite{Qiu} in the case of
on the Liouville theorem for bounded -harmonic maps from
complete Riemannian manifolds with non-negative -Ricci curvature
into regular geodesic balls of Riemannian manifolds with positive sectional
curvature upper bound. Finally, we establish a connection between the Liouville
property of -harmonic maps and the recurrence property of
-diffusion processes on manifolds. Our results are new even in the
case for