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Suppose that $M$ is a K\"ahler manifold with a pole such that its holomorphicsectional curvature is bounded from below by a constant and its radialsectional curvature is also bounded from below. Suppose that $N$ is a stronglypseudoconvex complex Finsler manifold such that its holomorphic sectionalcurvature is bounded from above by a negative constant. In this paper, weestablish a Schwarz lemma for holomorphic mappings $f$ form $M$ into $N$. Asapplications, we obtain a Liouville type rigidity result for holomorphicmappings $f$ from $M$ into $N$, as well as a rigidity theorem for bimeromorphicmappings from a compact complex manifold into a compact complex Finslermanifold.

Schwarz lemma from a K\"ahler manifold into a complex Finsler manifold