A Schwarz Lemma for Harmonic Mappings Between the Unit Balls in Real Euclidean Spaces

摘要

In this paper we prove a Schwarz lemma for harmonic mappings between the unitballs in real Euclidean spaces. Roughly speaking, our result says that under aharmonic mapping between the unit balls in real Euclidean spaces, the image ofa smaller ball centered at origin can be controlled. This extends the relatedresult proved by Chen in complex plane.