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

Abstract

The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane.

Keywords

Harmonic mappings / Schwarz lemma / Unit balls

References

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