A Schwarz-type lemma for squeezing functions on planar domains

With an easy application of the maximum principle, we establish a Schwarz-type lemma for the squeezing functions of finitely connected planar domains which bounds the squeezing functions in terms of invariants obtained from the canonical circularly slit representations of the domains. In particular, our result directly yields the explicit formulas for squeezing functions on doubly connected domains obtained by Ng, Tang and Tsai.