On the maximum principle on complete Finsler manifolds (Q386014)

The Omori-Yau maximum principle says that, for any complete, connected, noncompact Riemannian manifold \((M,g)\) with Ricci curvature bounded from below, if a \(C^2\) function \(\mathfrak{u}:M\longrightarrow R\) has an upper bound, then there exists a sequence \(x_k\) on \(M\) such that NEWLINE\[NEWLINE \lim\limits_{k\rightarrow\infty}\mathfrak{u}(x_k)=\sup_M \mathfrak{u}, \quad \lim\limits_{k\rightarrow\infty}|\nabla \mathfrak{u}| (x_k)=0, \quad \limsup\limits_{k\rightarrow\infty}\Delta \mathfrak{u}(x_k)\leq 0. NEWLINE\]NEWLINE The author of the present paper generalizes the Omori-Yau maximum principle to forward complete Finsler manifolds and gives some results about subharmonic functions on such manifolds.