Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove that if every bounded $\mathcal A$-harmonic function on a complete Riemannian manifold $M$ is asymptotically constant at infinity of $p$-nonparabolic ends of $M$, then each bounded $\mathcal A$-harmonic function is uniquely determined by the values at infinity of $p$-nonparabolic ends of $M$, where $\mathcal A$ is a nonlinear elliptic operator of type $p$ on $M$. Furthermore, in this case, every bounded $\mathcal A$-harmonic function on $M$ has finite energy.

Keywords: $\mathcal A$-harmonic function, end, $p$-parabolicity, uniqueness

MSC numbers: 58J05, 31B05